Well-posedness for stochastic scalar conservation laws with the initial-boundary condition

作者：Kobayasi Kazuo; Noboriguchi Dai^*

来源：Journal of Mathematical Analysis and Applications, 2018, 461(2): 1416-1458.

DOI：10.1016/j.jmaa.2018.01.054

• Stochastic partial differential equations
• Conservation laws
• Kinetic formulation
• Initial-boundary value problem

In this paper, we are interested in the initial-(non-homogeneous) Dirichlet boundary value problem for a multi-dimensional scalar non-linear conservation law with a multiplicative stochastic forcing. We introduce a notion of "renormalized" kinetic formulations in which the kinetic defect measures on the boundary of a domain are truncated. In such a kinetic formulation we establish a result of well-posedness of the initial-boundary value problem under only the assumptions (H-1), (H-2) and (H-3) stated below, which are very similar ones in [6].

• 出版日期2018-5-15