Velocity averaging for diffusive transport equations with discontinuous flux

Marko Erceg; Marin Mišur; Darko Mitrović

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arXiv · 2008.08310

Velocity averaging for diffusive transport equations with discontinuous flux

Marko Erceg·Marin Mišur·Darko Mitrović

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Abstract

We consider a diffusive transport equation with discontinuous flux and prove the velocity averaging result under non-degeneracy conditions. In order to achieve the result, we introduce a new variant of micro-local defect functionals which are able to ``recognise'' changes of the type of the equation. As a corollary, we show the existence of a weak solution for the Cauchy problem for nonlinear degenerate parabolic equation with discontinuous flux. We also show existence of strong traces at $t=0$ for so-called quasi-solutions to degenerate parabolic equations under non-degeneracy conditions on the diffusion term.

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Marko Erceg, Marin Mišur, Darko Mitrović. 2020-08-19. Velocity averaging for diffusive transport equations with discontinuous flux. https://arxiv.org/abs/2008.08310

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