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Perthame, B.; Souganidis, P. E.

A limiting case for velocity averaging. (English) Zbl 0956.45010

Ann. Sci. Éc. Norm. Supér. (4) 31, No. 4, 591-598 (1998).
Summary: We complete the theory of velocity averaging lemmas for transport equations by studying the limiting case of a full space derivative in the source term. Although the compactness of averages does not hold any longer, a specific estimate remains which shows compactness of averages in more general situations than those previously known. Our method is based on Calderón-Zygmund theory.

Cited in 43 Documents

MSC:

45K05 Integro-partial differential equations
82C70 Transport processes in time-dependent statistical mechanics
45M05 Asymptotics of solutions to integral equations

Keywords:

velocity averaging; transport equations; limiting case; compactness of averages; Calderón-Zygmund theory
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\textit{B. Perthame} and \textit{P. E. Souganidis}, Ann. Sci. Éc. Norm. Supér. (4) 31, No. 4, 591--598 (1998; Zbl 0956.45010)
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