A time splitting approach to quasilinear Degenerate Parabolic Partial Differential Equations
Analysis of PDEs
2016-06-07 v1
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 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.
Keywords
Cite
@article{arxiv.1606.01596,
title = {A time splitting approach to quasilinear Degenerate Parabolic Partial Differential Equations},
author = {Kazuo Kobayasi and Dai Noboriguchi},
journal= {arXiv preprint arXiv:1606.01596},
year = {2016}
}