engleski

The velocity averaging for a heat type equation

We prove that the sequence of averaged quantities $\int_{; ; ; ; \R^m}; ; ; ; h_n(t, x, \lambda) \rho(\lambda) d\lambda$ is strongly precompact in $L^1_{; ; ; ; loc}; ; ; ; (\R^+\times\R^d)$, where $\rho\in C_0(\R^m)$, and $h_n\in L^2(\R^+\times\R^d\times\R^m)$ are solutions to heat type equations with flux explicitly depending on space variables. The result is obtained by means of recently introduced parabolic H-measures.

velocity averaging; H-measures; heat type equation

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