Differential and Integral Equations

A time-splitting approach to quasilinear degenerate parabolic stochastic partial differential equations

Kazuo Kobayasi and 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, Hofmanová 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.

Article information

Source
Differential Integral Equations Volume 29, Number 11/12 (2016), 1139-1166.

Dates
First available in Project Euclid: 13 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.die/1476369333

Mathematical Reviews number (MathSciNet)
MR3557315

Zentralblatt MATH identifier
06674877

Subjects
Primary: 35L04: Initial-boundary value problems for first-order hyperbolic equations 60H15: Stochastic partial differential equations [See also 35R60]

Citation

Kobayasi, Kazuo; Noboriguchi, Dai. A time-splitting approach to quasilinear degenerate parabolic stochastic partial differential equations. Differential Integral Equations 29 (2016), no. 11/12, 1139--1166. https://projecteuclid.org/euclid.die/1476369333.


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