Energy dissipation admissibility condition for conservation law systems admitting singular solutions

نویسندگان

چکیده

The main goal of the paper is to define and use a condition sufficient choose unique solution conservation law systems with singular measure in initial data. Different approximations can lead solutions different distributional limits. new notion called backward energy then single out proper approximation definition based on maximal dissipation defined Dafermos (J Differ Equ 14:202–212, 1973). Suppose that system admits supplementary space–time divergent form where time component (strictly or not) convex function. It could be an density mathematical entropy gas dynamic models, for example. One admissibility conditions weak should maximally dissipate entropy. We show it consistent other case Riemann problems isentropic dynamics non-positive pressure first part paper. Singular these are described by shadow waves, nets piecewise constant respect variable. In second part, we apply those when data contains delta approximated functions.

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ژورنال

عنوان ژورنال: Nonlinear Differential Equations And Applications Nodea

سال: 2022

ISSN: ['1420-9004', '1021-9722']

DOI: https://doi.org/10.1007/s00030-022-00748-5