Naslov
Strong compactness of approximate solutions to degenerate elliptic-hyperbolic equations with discontinuous flux functions

Autori
Holden, Helge ; Karlsen, Kenneth ; Mitrovic, Darko ; Panov, Evgenii

Izvornik
Acta mathematica scientia (0252-9602) 29 (2009); 1573-1672

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
degenerate hyperbolic-elliptic equation; degenerate convection-diffusion equation; conservation law; discontinuous flux; approximate solutions; com- pactness

Sažetak
Under a non-degeneracy condition on the nonlinearities we show that se- quences 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.

Izvorni jezik
Engleski

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