arXiv subjects

Dai Noboriguchi

Publications and source records attributed to Dai Noboriguchi.

2 recordsLinked to original sources

arXiv2016

A time splitting approach to quasilinear Degenerate Parabolic Partial Differential Equations

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.

math.AP↗

arXiv2015

A stochastic conservation law with nonhomogeneous Dirichlet boundary conditions

This paper discusses the initial-boundary value problem (with a nonhomogeneous boundary condition) for a multi-dimensional scalar first-order conservation law with a multiplicative noise. One introduces a notion of kinetic formulations in which the kinetic defect measures on the boundary of a domain are truncated. In such a kinetic formulation one obtains a result of uniqueness and existence. The unique solution is the limit of the solution of the stochastic parabolic approximation.

math-ph↗