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
Publication date:
10.6.2011.
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