Project Details
Projekt
Analysis of energy-variational solutions for hyperbolic conservation laws
Applicants
Dr. Thomas Eiter; Dr. Robert Lasarzik
Subject Area
Mathematics
Term
since 2023
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 526018747
The goal of this project is to further develop the analytical theory of energy-variational solutions, which we introduced in a recent preprint for a general class of hyperbolic conservation laws. This notion of solution is a new generalized solvability concept, which relaxes the evolution equation to a variational inequality taking into account possible energy defects during the evolution. The framework provides a rich structure and comes along with several improved properties in comparison to previous solvability concepts: - existence of energy-variational solutions for a large class of models, - constructive existence proof via a minimizing-movement scheme, - weak-strong uniqueness and semi-flow property, - convexity and weak* closedness of the solution set, - in special cases: solution set continuously depends on the initial value. We aim to make new fundamental contributions to the analytical framework for this novel solution concept by extending it to a larger class of hyperbolic conservation laws and by comparing it to existing solvability frameworks like dissipative weak solutions and wild entropy solutions. Moreover, we plan to exploit the above properties to define appropriate criteria that select a unique physically reasonable candidate within the set of energy-variational solutions and to investigate the properties of this selection procedure. Furthermore, we use the selection criterion in the construction of approximation schemes.
DFG Programme
Priority Programmes
