Original scientific paper

The velocity averaging for a heterogeneous heat type equation

Martin Lazar orcid.org/0000-0002-4034-5770 ; University of Dubrovnik, Dubrovnik, Croatia
Darko Mitrović ; Faculty of Mathematics, University of Montenegro, Podgorica, Montenegro

Abstract

We prove that the sequence of averaged quantities
$\int_{\R^m}u_n(t,\mx,\my) v(\my)d\my$ is strongly precompact in
$\Ldl\Rjpd$, where $v\in \Ldc{\R^m}$, and $u_n\in
\Ld{\Rjpd\times \R^m}$ are solutions to strictly
parabolic transport equations with flux explicitly depending on
space and time. In order to obtain the result, we use a recently introduced parabolic variant of H-measures.

Keywords

velocity averaging; parabolic H-measures; heat type equation; heterogeneous coefficients

Hrčak ID:

68643

URI

https://hrcak.srce.hr/68643

Publication date:

10.6.2011.

Visits: 1.418 *