Research Interests

• Dissipative Systems in mathematical physics
• Nonlinear hyperbolic partial differential equations (systems, shock waves, stability, long-time existence)
• Fluid dynamics (compressible fluids, relativistic fluids with viscosity)
• Fluid-structure interaction (Interactions between viscous fluids and elastic solids, uniqueness)

Publications

Paper

1. Non-linear Stability of Shock Profiles in Dissipative Hyperbolic–Hyperbolic Systems, Arch. Ration. Mech. Anal. 250 Paper no.94 (2026) [pdf]
2. Global existence and asymptotic decay for small solutions of general quasilinear hyperbolic balance laws, J. Hyperbolic Differ. Equ. 22 613-642 (2025) [pdf]
3. Nonlinear stability of first-order relativistic viscous hydrodynamics, J. Math. Phys. 266 10 pp. (2025) [pdf]
4. Global existence and decay of small solutions for quasi-linear second-order uniformly dissipative hyperbolic-hyperbolic systems, J. Differential Equations 383, 130-162 (2024) [pdf]
5. With Heinrich Freistühler and Moritz Reintjes: Uniform dissipativity for mixed-order hyperbolic systems, with an application to relativistic fluid dynamics, J. Differential Equations 325, 70-81, (2022)
6. With Sebastian Schwarzacher: Weak-strong uniqueness for an elastic plate interacting with the Navier Stokes equation, SIAM J. Math. Anal. 54, 4104-4138 (2022) [pdf]
7. With Heinrich Freistühler: A class of uniformly dissipative symmetric hyperbolic-hyperbolic systems, J. Differ. Equations 288, 40-61 (2021).
8. Asymptotic stability in a second-order symmetric hyperbolic system modeling the relativistic dynamics of viscous heat-conductive fluids with diffusion. J. Differ. Equations 268, 825-851 (2020). [pdf]
9. Asymptotic stability of homogeneous states in the relativistic dynamics of viscous, heat-conductive fluids. Arch. Rational Mech. Anal. 231 (1), 91-113 (2019). [pdf]

PhD Thesis

1. Global existence and asymptotic decay for quasilinear second-order symmetric hyperbolic systems of partial differential equations occuring in the relativistic dynamics of dissipative fluids. PhD Thesis, University of Konstanz, (2019) [PDF],
   Supervisor: Prof. Dr. Heinrich Freistühler.

Master Thesis

1. Hilbertraumwertige Superlösungen stochastischer Rückwärts-Differentialgleichungen, Masterarbeit an der Universität Konstanz [PDF],
   Supervisors: Prof. Dr. Robert Denk and Prof. Dr. Michael Kupper .
   

These works where published under my previous name, Matthias Sroczinski.

Lectures at Conferences and Seminars:

Conferences

1. Invited speaker at Equadiff Conference 2024 (Karlstadt University)
2. Invited speaker at Workshop: Analysis of Dissipation in Inviscid and Compressible Fluid Dynamics (University of Konstanz, 2024)

Seminars

1. Invited speaker at PDE/ Apllied Math Seminar of Indiana Universtiy (Bloomington, IN, 2024)
2. Invited Speaker at CRC Seminar of KIT (Karlsruhe, 2024)
3. Invited speaker at PDE Seminar of Vanderbilt University (Nashville, TN, 2023)

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