STRONG COMPACTNESS OF APPROXIMATE SOLUTIONS TO DEGENERATE ELLIPTIC-HYPERBOLIC EQUATIONS WITH DISCONTINUOUS FLUX FUNCTION  

作　　者：Helge Holden Kenneth H. Karlsen Darko Mitrovic Evgueni Yu. Panov 

机构地区：[1]Department of Mathematical Sciences, Norwegian University of Science and Technology,NO–7491 Trondheim, Norway [2]Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern,NO–0316 Oslo, Norway [3]Centre of Mathematics for Applications, University of Oslo,P.O. Box 1053, Blindern, N–0316 Oslo, Norway [4]Faculty of Mathematics, University of Montenegro, 81000 Podgorica, Montenegro [5]Mathematical Analysis Department, Novgorod State University,ul. B. St. Peterburgskaya 41, 173003 Veliky Novgorod, Russia

出　　处：《Acta Mathematica Scientia》2009年第6期1573-1612,共40页数学物理学报（B辑英文版）

基　　金：supported by the Research Council of Norway through theprojects Nonlinear Problems in Mathematical Analysis; Waves In Fluids and Solids; Outstanding Young Inves-tigators Award (KHK), ;the Russian Foundation for Basic Research (grant No. 09-01-00490-a) ;DFGproject No. 436 RUS 113/895/0-1 (EYuP)

摘　　要：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.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.

关 键 词：degenerate hyperbolic-elliptic equation degenerate convection-diffusion equation conservation law discontinuous flux approximate solutions COMPACTNESS 

分 类 号：O175.28[理学—数学]