engleski

The velocity averaging for an ultra-parabolic heterogeneous equation

We prove that a sequence of averaged quantities $\int_{; ; ; \R^m}; ; ; h_n(x, \lambda)\rho(\lambda)d\lambda$, $n\in \N$, is strongly precompact in $L^1_{; ; ; loc}; ; ; (\R^d)$, where $\rho\in C_0(\R^m)$, and $h_n\in L^p(\R^d\times \R^m)$, $p\geq 2$, are solutions to an ultra-parabolic transport-type equation with continuously space-dependent coefficients.

velocity averaging; ultraparabolic H-measures; heterogeneous coefficients

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