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Advanced seminar AG Mathematical Modeling

Monday, 26.05.2025 at 17.00 in B7 - Room 210

 

Lecture by Thomas Eiter (WIAS Berlin) on the topic "Energy-variational solutions in the context of hyperbolic conservation laws".

Abstract: In general, the global-in-time existence of weak solutions to hyperbolic conservation laws is only known in the scalar or the one-dimensional case. Due to the lack of analogous results for multi-dimensional systems, more generalized solvability concepts have been introduced in the last decades. In this talk, we consider the notion of energy-variational solutions, which relaxes the weak formulation to an inequality that is preserved under weak convergence. We discuss the analytic construction of these solutions by a time-discrete minimizing-movements scheme, which does not require any spatial regularization. Furthermore, we study properties like weak-strong uniqueness and the structure of the solution set. With a particular focus on the Euler equations, we further discuss the long-time behavior of energy-variational solutions and their relation to other modern solvability concepts.

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