×

zbMATH — the first resource for mathematics

Strong compactness of approximate solutions to degenerate elliptic-hyperbolic equations with discontinuous flux function. (English) Zbl 1212.35166
Summary: Under a non-degeneracy condition on the nonlinearities we show that sequences of approximate entropy solutions of mixed elliptic-hyperbolic equations are strongly precompact in the general case of a Caratheodory flux vector. The proofs are based on deriving localization principles for \(H\)-measures associated to sequences of measure-valued functions. This main result implies existence of solutions to degenerate parabolic convection-diffusion equations with discontinuous flux. Moreover, it provides a framework in which one can prove convergence of various types of approximate solutions, such as those generated by the vanishing viscosity method and numerical schemes.

MSC:
35J70 Degenerate elliptic equations
35K65 Degenerate parabolic equations
35L65 Hyperbolic conservation laws
35B25 Singular perturbations in context of PDEs
PDF BibTeX XML Cite
Full Text: DOI