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Photos of Group

Photo of the Applied PDE group, July 2024 Members of the Applied PDE group presented in the Conference HYP2022 "International Conferences on Hyperbolic Problems, Theory, Numerics and Applications”, June 2022. Photo of the Applied PDE group, November 2018

Publications

papers

Publications

Publications 2024 Alves, N. J., Grafakos, L., & Tzavaras, A. E. (2024). A bilinear fractional integral operator for Euler-Riesz systems. handle arxiv Alves, N. J., Skrzeczkowski, J., & Tzavaras, A. E. (2024). Strong convergence of sequences with vanishing relative entropy. handle arxiv Kim, H., Lee, K. K., Firisa, G., Lee, J., Choi, M. C., & Kim, Y.-J. (2024). Fractionation by Spatially Heterogeneous Diffusion: Experiments and the Two-Component Random Walk Model. Journal of the American Chemical Society, 146(37), 25544–25551. handle doi Georgiadis, S. (2024). Energy identity for the

Teaching

Teaching

Courses Real Analysis - AMCS 235 This is a basic introductory graduate level course on Real Analysis. It starts with a review of notions connected with the real analysis of continuous functions including the Ascoli-Arzela Theorem on compactness of sequences of continuous functions, and the Stone-Weierstrass Theorem for the approximation of continuous functions. The main body of the course will be the theory of measure and integration. The last part of the course deals with various topics in Real Analysis, like Differentiation, approximation of $L^p$ functions, and Fourier Series. The

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Applied PDE Research Group

Applied Partial Differential Equations Research Group Professor Athanasios Tzavaras leads the Applied PDE group, which stands for Applied Partial Differential Equations Research group areas of expertise and current scientific interests: analysis of partial differential equations, mathematical modeling, and numerical methods Our group is interested in mathematical modeling, analysis and the development of numerical methods for evolutionary partial differential equations in fluid and solid mechanics. Subjects of current interest include: Relative entropy and the comparison of thermomechanical

Other

Research topics

Effect of anisotropic diffusivity, development of gradients due to discontinuities in diffusivity Diffusion of multicomponent systems, cross diffusion systems, mathematical properties, renormalized solutions, uniqueness of weak solutions. Thermodynamics, Soret effect, diffusion of binary liquid, heterogeneous diffusion equation.

visitors

Visitors

Visitors 2024 Dr. Anastasia Molchanova, Postdoctoral Fellow, Institute of Analysis and Scientific Computing, TU Wien, Austria October 2024 Mathematics and Applications Colloquium Sobolev Homeomorphisms in Nonlinear Elasticity Seminar Limits of Sobolev Homeomorphisms: Injectivity Zainab Alalawi, Boston University, USA Summer 2024 Professor Yong-Jung Kim, KAIST, Korea February 2024 Mathematics and Applications Colloquium Diffusion with Heterogeneous Persistence and Permeability Minyoo Kim, KAIST, Korea February 2024 2023 Professor Suleyman Ulusoy, School of Arts and Sciences, American University

Visitors old

Visitors 2023 Professor Jose Carrillo, University of Oxford, UK January 8th - January 19th Mathematics and Applications Colloquium AMCS CEMSE Nonlocal Aggregation-Diffusion Equations: entropies, gradient flows, phase transitions and applications Prof. Jose Carrillo, Department of Mathematics, University of Oxford, UK Tuesday, January 10, 2023, 15:30 - 17:00 Building 2, Level 5, Room 5209 Fokker-Planck equations Cucker-Smale orientation dynamics McKean-Vlasov equations Keller-Segel-type models Contact Person Athanasios Tzavaras This talk will be devoted to an overview of recent results in