engleski

The velocity averaging for a heterogeneous heat type equation

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 a strictly parabolic transport equations with flux explicitly depending on space. In order to obtain the result, we use recently introduced parabolic variant of the H-measures.

parabolic H-measures; velocity averaging; heterogeneous heat equation

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