Naslov
Hyperbolic conservation laws with vanishing nonlinear diffusion and linear dispersion in heterogeneous media

Autori
Aleksić, Jelena ; Mitrović, Darko ; Pilipović, Stevan

Izvornik
Journal of evolution equations (1424-3199) 9 (2009); 809-1

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

Ključne riječi
heterogeneous conservation law; diffusion-dispersion limit; H-measures

Sažetak
We show strong precompactness of the familly of solutions to scalar conservation laws with vanishing diffusion and dispersion. The basic tools are the H-measures. We analyze family of solutions to multidimensional scalar conservation law, with flux depending on the time and space explicitly, regularized with vanishing diffusion and dispersion terms. Under a condition on the balance between diffusion and dispersion parameters, we prove that the family of solutions is precompact in L1loc. Our proof is based on the methodology developed in Sazhenkov (Sibirsk Math Zh 47(2):431–454, 2006), which is in turn based on Panov’s extension (Panov and Yu in Mat Sb 185(2):87–106, 1994) of Tartar’s H-measures (Tartar in Proc R Soc Edinb Sect A 115(3–4):193–230, 1990), or Gerard’s micro-local defect measures (Gerard Commun Partial Differ Equ 16(11):1761–1794, 1991). This is new approach for the diffusion–dispersion limit problems. Previous results were restricted to scalar conservation laws with flux depending only on the state variable.

Izvorni jezik
Engleski

POVEZANOST RADA