Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4664914 | Acta Mathematica Scientia | 2009 | 40 Pages |
Abstract
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 measurevalued 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)