A time splitting approach to quasilinear Degenerate Parabolic Partial Differential Equations

Kazuo Kobayasi; Dai Noboriguchi

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arXiv · 1606.01596

A time splitting approach to quasilinear Degenerate Parabolic Partial Differential Equations

Kazuo Kobayasi·Dai Noboriguchi

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Abstract

In this paper, we discuss the Cauchy problem for a degenerate parabolic hyperbolic equation with a multiplicative noise. We focus on the existence of a solution. Using nondegenerate smooth approximations, Debussche, Hofmanov\'a and Vovelle [8] proved the existence of a kinetic solution. On the other hand, we propose to construct a sequence of approximations by applying a time splitting method and prove that this converges strongly in $L^1$ to a kinetic solution. This method will somewhat give us not only a simpler and more direct argument but an improvement over the existence result.

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Kazuo Kobayasi, Dai Noboriguchi. 2016-06-06. A time splitting approach to quasilinear Degenerate Parabolic Partial Differential Equations. https://arxiv.org/abs/1606.01596

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