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Applied Analysis

ABOUT    R&D ACTIVITIES    R&D PROGRAMS    PEOPLE    PUBLICATIONS


ABOUT

The field of Applied Analysis brings together several mathematical topics of great interest and aims at investigating, among others, partial differential equations, probability theory, stochastic partial differential equations, infinite dynamical systems of ordinary differential equations and stochastic analysis. More specifically, the group studies rigorously the dynamics of interfaces for certain reaction-diffusion equations both deterministic and stochastic, sharp interface limits and conservation laws under mean curvature flow. The physical background is diverse, and is stemming mainly from problems of phase transitions, and mathematical physics. Morevover, the group studies large-scale systems of interacting particles and their hydrodynamic limits to model and to rigorously analyze complex systems arising in engineering sciences and physics. The group works towards novel and rigorous results and particular attention is paid to the training of graduate students and postdocs.


RESEARCH AND DEVELOPMENT ACTIVITIES

Partial differential equations and stochastic differential equations: The interaction between the theory of partial differential equations and probability is very fruitful for research in mathematics, both because of the intrinsic mathematical challenges presented, and because of the range of applications. The study of evolution equations with a stochastic forcing has seen major advances in the recent years. Applications include a variety of important reaction-diffusion equations arising in mathematical physics, but the potential for development of this theory in other applications, such as mathematical finance, mathematical biology and others, is enormous. Research in this direction aims at developing innovative analysis suitable for a rigorous mathematical study of the effects of thermal fluctuations. These include among others the study of stochastic reaction-diffusion equations, motion by mean curvature with random forcing, Malliavin calculus, applications to finance and others.

Integrable Systems: We have analyzed so-called “completely integrable” infinite dimensional Hamiltonian systems, in  particular partial differential equations and nonlinear lattices (large systems of ODEs). We have been particularly interested in asymptotic problems like the investigation of long time asymptotics, semiclassical asymptotics, zero dispersion limits and continuum limits of solutions of initial and initial-boundary value problems for nonlinear dispersive partial differential equations and nonlinear lattices, including difficult problems involving instabilities. We have used and extended techniques from PDE theory, complex analysis, harmonic analysis, potential theory and algebraic geometry. Along the way, we have made contributions to the analysis of Riemann-Hilbert factorization problems on the complex plane or a hyperelliptic Riemann surface and the related theory of variational problems for Green potentials with harmonic external fields. In a sense we have worked on a “nonlinear microlocal analysis” that generalizes the classical theory of stationary phase and steepest descent.

Large Scale Stochastic Dynamics: Interacting particle systems are models with many degrees of freedom whose stochastic dynamics is prescribed at a microscopic scale. Such models have been very successful in modelling and rigorously analyzing complex systems motivated by engineering sciences, physics, and finance. The aim is to understand and to derive quantitative effective descriptions of phenomena that emerge on the macroscopic scale, and to relate macroscopic observables of these systems to the parameters of their microscopic interactions. 

Education and Training: The group contributes to the education and training of undergraduate, graduate and post-graduate students as well as of PhD candidates and Postdoctoral researchers.


RESEARCH AND DEVELOPMENT PROGRAMS

A. ONGOING PROJECTS

  • Title: IPMAFIN: Interfacial phenomena in stochastic reaction-diffusion systems & applications to mathematical finance
    Funding Source and funding scheme: Hellenic Foundation for Research and Innovation (H.F.R.I.) under the “Basic Research Financing Action (Horizontal support of all Sciences), Subaction II, Greece 2.0
    Duration: 2023-2025
  • Title: HYDRODYNAMIC: Hydrodynamic limit of phase separating interacting particle systems
    Funding Source and funding scheme: Hellenic Foundation for Research and Innovation (H.F.R.I.)
    Duration: 2021-2025

B. COMPLETED PROJECTS

  • Title: iSTAMP: Innovative Stochastic  Dynamics, Analysis and Simulations for Phase Transitions
    Funding Source and funding scheme: Hellenic Foundation for Research and Innovation (H.F.R.I) under the “First Call for H.F.R.I. Research Projects to support Faculty members and Researchers”
    Duration: 2020-2023


PEOPLE


PUBLICATIONS

  • DC Antonopoulou, D Farazakis, G Karali (2026) Asymptotics for the ϵ-Cahn-Hilliard/Allen-Cahn with deterministic or stochastic forcing, Communications in Mathematical Sciences 24 (2), 499-520.
  • A Chatziafratis, G Karali, CE Synolakis (2026) Rigorous Analytical Solution for the Linearized Whitham–Broer–Kaup System on the Half‐Line, Studies in Applied Mathematics 156 (6), e70237, https://doi.org/10.1111/sapm.70237
  • D Dimitriou, D Farazakis, G Karali (2026) Malliavin Calculus for the stochastic Cahn-Hilliard equation driven by fractional noise, arXiv preprint arXiv:2601.10490
  • G Karali, A Stavrianidi, K Tzirakis, P Zoubouloglou (2026) On the density of the supremum of nonlinear SPDEs, arXiv preprint arXiv:2603.12186

  • DC Antonopoulou, G Dewhirst, G Karali, K Tzirakis (2025) Local existence of the outer parabolic stochastic Stefan problem on the sphere, Journal of Differential Equations 423, 439-475.
  • DC Antonopoulou, D Farazakis, G Karali (2025) Existence of maximal solutions for the financial stochastic Stefan problem of a volatile asset with spread, Stochastic Processes and their Applications 179, 104506 (pdf file)
  • DC Antonopoulou, G Karali, D Li (2025) Optimal Error Estimates of Energy-Stable Runge–Kutta Methods for the ε-dependent Cahn-Hilliard/Allen-Cahn Equation, Journal of Scientific Computing 103 (2), 1-31.
  • G Barbatis, M Chatzakou, A Tertikas (2025) Geometric Hardy inequalities on the Heisenberg groups via convexity, arXiv preprint arXiv:2503.08383
  • A Chatziafratis, S Kamvissis (2025) Infinity of solutions to initial‐boundary value problems for linear constant‐coefficient evolution PDEs on semi‐infinite intervals, Bulletin of the London Mathematical Society, https://doi.org/10.1112/blms.70179
  • A Chatziafratis, A Miranville, G Karali, AS Fokas, EC Aifantis (2025) Higher-order diffusion and Cahn-Hilliard-type models revisited on the half-line, Mathematical Models and Methods in Applied Sciences, 35 (5), 1133, https://doi.org/10.1142/S0218202525500101
  • S Filippas, L Moschini, A Tertikas (2025) Liouville type properties for a class of weighted anisotropic elliptic equations, Calculus of Variations and Partial Differential Equations 64 , 263, https://doi.org/10.1007/s00526-025-03072-9
  • S Filippas, A Tertikas (2025) Best constants for weighted Hardy inequalities in the exterior of balls and circular cylinders, Nonlinear Analysis 261, 113885.
  • S Filippas, A Tertikas (2025) Lp Hardy inequalities in the exterior of a ball, (pdf file)
  • G Karali, K Tzirakis, IM Sigal (2025) The FitzHugh-Nagumo system on undulated cylinders: spontaneous symmetrization and effective system, Journal of Nonlinear Science 35 (3), 64.
  • D Sofikitis, L Reichwein, MG Stamatakis, C Zois, DG Papazoglou, S Cohen, M Büscher, A Pukhov, TP Rakitzis (2025) High-energy polarized electron beams from the ionization of isolated spin polarized hydrogen atoms, Physical Review A, 111, 053119, DOI: https://doi.org/10.1103/PhysRevA.111.053119
  • CS Vrettou, M Loulakis (2025) Ventilator-induced signal interference and the accuracy of the pressure reactivity index in acute brain injury, https://doi.org/10.21203/rs.3.rs-7608547/v1

  • ND Alikakos, Z Geng (2024) On the Triple Junction Problem without Symmetry Hypotheses, Archive for Rational Mechanics and Analysis 248 (2), 24.
  • ND Alikakos, M Nikolouzos, AN Yannacopoulos (2024) Variational maximum principle for elliptic systems involving the fractional Laplacian, São Paulo Journal of Mathematical Sciences, 1-20.
  • DC Antonopoulou, D Dimitriou, G Karali, K Tzirakis (2024) Malliavin Calculus for the one-dimensional Stochastic Stefan Problem, arXiv preprint arXiv:2407.20389
  • G Barbatis, KT Gkikas, A Tertikas (2024) Heat and Martin kernel estimates for Schrödinger operators with critical Hardy potentials, Mathematische Annalen 389 (3), 2123-2192.
  • G Barbatis, A Tertikas (2024) Sobolev improvements on sharp Rellich inequalities, Journal of Spectral Theory 14 (2024), 641–663, DOI 10.4171/JST/508
  • J.L. Bona, A. Chatziafratis, H. Chen, S. Kamvissis (2024) The linear BBM-equation on the half-line, revisited,  Letters in Mathematical Physics, Vol. 114, 91, https://doi.org/10.1007/s11005-024-01820-0
  • A Chatziafratis, S Kamvissis (2024) A note on uniqueness for linear evolution PDEs posed on the quarter-plane, arXiv preprint arXiv:2401.08531
  • A Chatziafratis, S Kamvissis (2024) Continuous dependence on data for linear evolution PDEs on the quarter-plane, arXiv preprint arXiv:2403.14323
  • A Chatziafratis, L Grafakos, S Kamvissis (2024) Long-Range Instability of Linear Evolution PDE on Semi-Bounded Domains via the Fokas Method, Dynamics of PDE, Vol. 21, No. 2, 97-169 (pdf file)
  • D Farazakis, G Karali, A Stavrianidi (2024) Malliavin Calculus for the stochastic heat equation and results on the density, arXiv preprint arXiv:2410.10115
  • S Filippas, L Moschini, A Tertikas (2024) Liouville type properties for a class of weighted anisotropic elliptic equations, (pdf)
  • N Hatzizisis, S Kamvissis (2024) Semiclassical WKB problem for the non-self-adjoint Dirac operator with a multi-humped decaying potential, Asymptotic Analysis, vol. 137, no. 3-4, pp. 177-243.
  • A Koutsimpela, M Loulakis (2024) On the optimally controlled stochastic shallow lake, International Journal of Control 97 (11), 2539-2551.
  • A Koutsimpela, M Loulakis (2024) Optimal control, viscosity approximation and Arrhenius Law for the shallow lake problem, arXiv preprint arXiv:2401.07642

  • Alikakos N., Geng Z. (2023) On the triple junction problem with general surface tension coefficients, arXiv preprint arXiv:2304.13106
  • Antonopoulou D., Farazakis D., Karali G. (2023) Existence of maximal solutions for the financial stochastic Stefan problem of a volatile asset with spread, arXiv preprint arXiv:2302.09841  
  • Antonopoulou D., Karali G., D. Li  (2023) Linearized Runge-Kutta methods for the ε-dependent Cahn-Hilliard/Allen-Cahn equation, preprint 
  • Barbatis, G., Gkikas, K.T.,  Tertikas, A. (2023) Heat and Martin Kernel estimates for Schrödinger operators with critical Hardy potentials. Math. Ann., https://doi.org/10.1007/s00208-023-02693-9
  • G Barbatis, A Tertikas (2023) Sobolev improvements on sharp Rellich inequalities, arXiv preprint arXiv:2312.00433
  • Filippas, S., Tersenov, A. (2023) Estimates on the velocity of a rigid body moving in a fluid, arXiv preprint arXiv:2304.11887
  • S Fujiié, N Hatzizisis, S Kamvissis (2023) Semiclassical WKB problem for the non-self-adjoint Dirac operator with an analytic rapidly oscillating potential, Journal of Differential Equations, Vol. 360, pp. 90-150. (html file)
  • N Hatzizisis, S Kamvissis (2023) Semiclassical WKB problem for the non-self-adjoint Dirac operator with a multi-humped decaying potential, Asymptotic Analysis, vol. 137, no. 3-4, pp. 177-243.
  • R Kousovista, G Karali, V Karalis (2023) Modeling the Double Peak Phenomenon in Drug Absorption Kinetics: The Case of Amisulpride, BioMedInformatics 3 (1), 177-192.

  • Antonopoulou D., Bitsaki M., Karali G. (2022) The multi-dimensional stochastic Stefan financial model for a portofolio of assets, Discrete Contin. Dyn. Syst.- Ser. B, 4, 1955-1987, (pdf)
  • A Chatziafratis, S Kamvissis, I Stratis (2022) Boundary behavior of the solution to the linear Korteweg‐De Vries equation on the half line, Studies in Applied Mathematics, Wiley Online Library, https://doi.org/10.1111/sapm.12542
  • S Fujiie, N Hatzizisis, S Kamvissis (2022) Semiclassical Wkb Problem for the Non-Self-Adjoint Dirac Operator Withan Analytic Rapidly Oscillating Potential, Available at SSRN 4108409 (html)
  • PD Karageorge, GN Makrakis (2022) Asymptotic approximations for the phase space Schrödinger equation, Journal of Physics A: Mathematical and Theoretical 55 (34), 345201.

  • Alikakos N., Gazoulis D., Zarnescu A. (2021) Entire Minimizers of Allen–Cahn Systems with Sub-Quadratic Potentials, Journal of Dynamics and Differential Equations, https://doi.org/10.1007/s10884-021-10092-4
  • Antonopoulou, D., Karali, G., Tzirakis, K. (2021) Layer dynamics for the one dimensional ε-dependent Cahn-Hilliard/Allen-Cahn equation, Calc. Var. Partial Differential Equations, 60, 207.
  • Filippas, S., Tersenov, A. (2021) On Vector Fields Describing the 2d Motion of a Rigid Body in a Viscous Fluid and Applications, J. Math. Fluid Mech. 23, 5 . https://doi.org/10.1007/s00021-020-00528-0
  • Hatzizisis, N., Kamvissis, S., (2021) Semiclassical WKB problem for the non-self-adjoint Dirac operator with a decaying potential, Journal of Mathematical Physics, v. 62, n. 3, 033510.
  • N Hatzizisis, S Kamvissis (2021) On Soliton Resolution for a Lattice, arXiv preprint arXiv:2106.07974
  • PD Karageorge, GN Makrakis (2021) The Anisotropic Gaussian Semi-Classical Schrödinger Propagator, arXiv preprint arXiv:2108.11077
  • R Kousovista, G Karali, K Vlasopoulou, V Karalis (2021) Validation of population pharmacokinetic models: a comparison of internal and external validation approaches for hydrochlorothiazide, Xenobiotica 51 (12), 1372-1388.

  • DC Antonopoulou, M Bitsaki, G Karali (2020) The multi-dimensional Stochastic Stefan Financial Model for a portfolio of assets, arXiv preprint arXiv:2012.13432
  • Cheliotis, D., Loulakis, M., Kontoyiannis, I., Toumpis, S. (2020) ‘A Simple Network of Nodes Moving on the Circle, Random Struct Alg 2020. DOI:10.1002/rsa.20932
  • Fujiie, S., Kamvissis, S., (2020) Semiclassical WKB problem for the non-self-adjoint Dirac operator with analytic potential, Journal of Mathematical Physics, v.61, n.1, 011510.
  • Haskovec, J. Markou, I., (2020) Asymptotic flocking in the Cucker-Smale model with reaction-type delays in the non-oscillatory regime, Kinet. Relat. Models 13, 795—813.
  • Haskovec, J., Markou, I., (2020) Exponential asymptotic flocking in the Cucker-Smale model with distributed delays, Math. Biosci. Eng., 17, 5651—5671.

  • Loulakis, M., Kossioris G.T., Souganidis, P.E., (2019) The Deterministic and Stochastic Shallow Lake Problem. In: Friz P., König W., Mukherjee C., Olla S. (eds) Probability and Analysis in Interacting Physical Systems, in honor of S.R.S. Varadhan 75th birthday, Springer 2019, 49-74. DOI:10.1007/978-3-030-15338-0_3210
  • Mouloudakis, K., Loulakis, M., Kominis, I.K., (2019) Quantum trajectories in spin-exchange collisions reveal the nature of spin-noise correlations in multispecies alkali-metal vapors, Phys. Rev. Research 1, 033017, DOI:10.1103/PhysRevResearch.1.03301

  • M Alfaro, D Antonopoulou, G Karali, H Matano (2018) Generation of fine transition layers and their dynamics for the stochastic Allen–Cahn equation, arXiv preprint arXiv:1812.03804
  • Alikakos, N., Fusco, G., Smyrnelis, P., (2018) Elliptic systems of phase transition type, Monograph, PNLDE, Volume 91, 2018, Birkhauser, 343 pages.
  • Alikakos, N., Fusco, G., (2018) Almost entire solutions of the Burgers equation, Electron.J. Differ. Eq., no 53, pp 1-6.
  • Antonopoulou, D., Blomker, D., Karali, G., (2018) The sharp interface limit for the stochastic Cahn-Hilliard equation, Annales Inst. Henri Poincare Probab. and Stat., 54, no 1, 280-298.
  • Antonopoulou, D., Farazakis, D., Karali, G., (2018) Malliavin Calculus for the stochastic Cahn-Hilliard/Allen-Cahn equation with unbounded noise diffusion, J. Differential Equations, 265, no 7, 3168-3211.
  • Barbatis, G., Filippas, S., Tertikas, A. (2018) ‘Sharp Hardy and Hardy–Sobolev inequalities with point singularities on the boundary’, Journal des Mathematiques Pures et Appliquees, 2018, 117, pp. 146–184.
  • Bates, P., Fusco, G., Karali, G., (2018) Gradient dynamics: motion near a manifold of quasi-equilibria, SIAM Journal on Applied Dynamical Systems, 17, no 3, 2106-2145.
  • Markou, I., (2018) Collision-avoiding in the singular Cucker-Smale model with nonlinear velocity couplings, Discrete Contin. Dyn. Syst. 38, 5245-5260.

  • Armendariz, I., Grosskinsky, S. and Loulakis, M., (2017). Metastability in a Condensing Zero Range Process in the Thermodynamic Limit, Probab. Th. Rel. Fields 169, no. 1-2, 105-175.
  • Cheliotis, D., Kontoyiannis, I., Loulakis, M. and Toumpis, S., (2017). Exact Speed and Transmission Cost in a Simple One-Dimensional Wireless Delay-Tolerant Network, IEEE ISIT 2017, pp 476-480.
  • KS Giannopoulou, GN Makrakis (2017) An approximate series solution of the semiclassical Wigner equation, arXiv preprint arXiv:1705.06754
  • Loulakis, M., Blatsios, G., Vrettou, C.S., Kominis, I.K., (2017). Quantum Biometrics with Retinal Photon Counting, Phys. Rev. Applied 8, 044012.

  • Alikakos, N.D.; Fusco, G. (2016), Asymptotic behavior and rigidity results for symmetric solutions of the elliptic system Δu=Wu(u), Annali della Scuola Normale Superiore di Pisa. XV issue special (2016), pp. 809-836.
  • Antonopoulou, D., Bates, P. Blomker, D., Karali, G., Millet, A., (2016). Motion of a droplet for the stochastic mass-conserving Allen-Cahn equation, SIAM J. Math. Anal. 48, no 1, 670-708.
  • Antonopoulou, D., Karali, G., Millet, A., (2016). Existence and regularity of solution for a Stochastic Cahn-Hilliard/Allen-Cahn equation with un-bounded noise diffusion, J. Differential Equations, 260, 2383-2417, (2016).
  • Loulakis, M., (2016). Introduction to Mathematical Finance, Hellenic Academic Libraries available at http://hdl.handle.net/11419/3481
  • Loulakis, M., (2016). Stochastic Processes, Hellenic Academic Libraries available at http://hdl.handle.net/11419/6003

  • Alikakos, ND.; Fusco, G. (2015), A maximum principle for systems with variational structure and an application to standing waves, Journal of the European Mathematical Society 17, No. 7 (2015), pp. 1547-1567.
  • Antonopoulou, D.C., Kamvissis, S., (2015). On the Dirichlet to Neumann Problem for the 1 dimensional Cubic NLS Equation on the Half-Line, Nonlinearity, v. 28, pp. 3073-3099.
  • Antonopoulou, D., Karali, G., Plexousakis, M., Zouraris, G., (2015). Crank-Nicolson finite element discretizations for a 2d linear Schrodinger-type equation posed in a noncylindrical domain, Mathematics of Computation, 84, no 294, 1571-1598.
  • G Barbatis, A Tertikas (2015) On the Hardy constant of some non-convex planar domains, Geometric Methods in PDE’s, 15-41.
  • J Dolbeault, MJ Esteban, S Filippas, A Tertikas (2015) Rigidity results with applications to best constants and symmetry of Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities, Calculus of Variations and Partial Differential Equations 54, 2465-2481.
  • Kamvissis, S., Shepelsky, D., Zielinski, L., (2015). Robin boundary condition and shock problem for the focusing nonlinear Schroedinger equation, Journal of Nonlinear Mathematical Physics, v. 22, n. 3, 2015, pp. 448-473.
  • Karali, G., Sourdis, C., (2015). The ground state of a Gross-Pitaevskii energy with general potential in the Thomas-Fermi limit, Archive for Rational Mechanics and Analysis, 217, no 2, 439-523.
  • Stai, E., Loulakis, M., Papavassiliou, S., (2015). Cross-Layer Design of Wireless Multihop Networks over Stochastic Channels with Time-Varying Statistics, IEEE Trans. Wireless Commun. 14, no. 12, 6967-6980.

  • Antonopoulou, D., Karali, G., Orlandi, E., (2014). A Hilbert expansion method for the rigorous sharp interface limit of the generalized Cahn-Hilliard equation, Interfaces and Free Boundaries, 16, 65-104.
  • G Barbatis, A Tertikas (2014) On the Hardy constant of non-convex planar domains: the case of the quadrilateral, Journal of Functional Analysis 266 (6), 3701-3725.
  • N Benas, N Chrysoulakis, N Christakis, G Kossioris, M Plexousakis (2014) WRF input parameter updates based on recent and long-term satellite observations, Proceedings of the 12th International Conference of Meteorology, Climatology and Physics of the Atmosphere (COMECAP 2014), 28-31.
  • N Christakis, T Katsaounis, G Kossioris, M Plexousakis (2014) On the performance of the WRF numerical model over complex terrain on a high performance computing cluster, 2014 ieee intl conf on high performance computing and communications.
  • N Christakis, T Katsaounis, G Kossioris, M Plexousakis (2014) Evaluation of WRF performance for the analysis of surface wind speeds over various Greek regions, https://core.ac.uk/download/pdf/20257788.pdf
  • Dellis, A.T., Loulakis, M., Kominis, I.K., (2014).Spin-noise correlations and spin-noise exchange driven by low-field spin-exchange collisions, Phys Rev A, 90 (3), 032905.
  • Dobrokhotov, S.Y., Makrakis, G.N. and Nazaiksinskii, V.E., (2014). Maslov’s Canonical Operator, Hörmander’s Formula, and Localization of Berry–Balazs’ Solution in the Theory of Wave Beams, Theoretical and Mathematical Physics, Vol. 180, No. 3, pp. 162-182.
  • Dobrokhotov, S.Y., Makrakis, G.N. and Nazaiksinskii, V.E., (2014). Fourier integrals and a new representation of Maslov’s canonical operator near caustics, Spectral theory and differential equations 233, 95-115.
  • S Filippas, L Moschini, A Tertikas (2014) Trace Hardy–Sobolev–Mazy’a inequalities for the half fractional Laplacian, arXiv preprint arXiv:1409.4519
  • SK Giannopoulou, GN Makrakis (2014) Uniformization of WKB functions by Wigner transform Applicable Analysis 93 (3), 624-645.
  • EK Kalligiannaki, GN Makrakis (2014) Perturbation solutions of the semiclassical Wigner equation, arXiv preprint arXiv:1402.6194
  • PD Karageorge, GN Makrakis (2014) Asymptotic Solutions of the Phase Space Schrödinger Equation: Anisotropic Gaussian Approximation, arXiv preprint arXiv:1402.6854
  • Karali, G., Nagase, Y., (2014). On the existence of solution for a Cahn-Hilliard/Allen-Cahn equation, Discrete Contin. Dyn. Syst.- Ser. S, 7, no 1, 127-137.
  • GN Makrakis (2014) Formal asymptotic expansion of the Faddeev-Green function in unbounded domains, arXiv preprint arXiv:1402.4641

  • Alikakos, ND., (2013), On the structure of phase transition maps for three or more coexisting phases. In Geometric partial differential equations M. Novaga and G. Orlandi eds. Publications of the Scuola Normale Superiore, CRM Series, Birkhauser.
  • Alikakos, ND.; Antonopoulos, P; Damialis, A (2013), Plateau angle conditions for the vector-valued Allen, SIAM Journal on Mathematical Analysis 45 No. 6 (2013), pp. 3823-3837.
  • Antonopoulou, D., Karali, G., (2013). A nonlinear partial differential equation for the volume preserving mean curvature flow, Networks and Heterogenous Media, 8 no 1, 9-22.
  • Armendariz, I., Grosskinsky, S. and Loulakis, M., (2013). Zero Range Condensation at Criticality, Stoch. Proc. and Appl. 123, no. 9, 3466-3496.
  • Dobrokhotov, S.Y., Makrakis, G.N., Nazaikinskii, V.E. and Tudorovskii, T.Y., (2013). New formulas for Maslov’s canonical operator in a neighborhood of focal points and caustics in 2D semiclassical asymptotics, Theoretical and Mathematical Physics, Vol. 177, No. 3, pp. 1579-1605.
  • S Filippas, L Moschini, A Tertikas (2013) Sharp Trace Hardy–Sobolev-Maz’ya Inequalities and the Fractional Laplacian, Archive for Rational Mechanics and Analysis 208 (1), 109-161
  • Giannopoulou, S.K. and Makrakis, G.N., (2013). Uniformization of WKB functions by Wigner transform, Applicable Analysis (Published online: DOI:10.1080/00036811.2013.794939).
  • Karali, G., Suzuki, T., Yamada, Y., (2013). Global-in-time behavior of the solution to a Gierer-Meinhardt system, Discrete Contin. Dyn. Syst.- Ser. A, 33 no 7, 2885–2900.
  • Kossioris, G.T.; Zouraris, G.E. (2013). Finite element approximations for a linear fourth-order parabolic SPDE in two and three space dimensions with additive space-time white noise. Appl. Numer. Math. 67, 243–261.
  • Kossioris, G.T.; Zouraris, G.E. (2013). Finite element approximations for a linear Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise. Discrete Contin. Dyn. Syst. Ser. B 18, no. 7, 1845–1872.

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