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Oberseminar AG Mathematische Modellierung
Montag, den 26.05.2025 um 17.00 Uhr in B7 - Raum 210
Vortrag von Thomas Eiter (WIAS Berlin) zum Thema „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. Moreover, 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.