TY - JOUR
T1 - Well-posedness for stochastic scalar conservation laws with the initial-boundary condition
AU - Kobayasi, Kazuo
AU - Noboriguchi, Dai
N1 - Funding Information:
This work was partially supported by JSPS Grants-in-Aid No. 16H03948 and No. 16K05212 .
Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2018/5/15
Y1 - 2018/5/15
N2 - 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 (H1), (H2) and (H3) stated below, which are very similar ones in [6].
AB - 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 (H1), (H2) and (H3) stated below, which are very similar ones in [6].
KW - Conservation laws
KW - Initial-boundary value problem
KW - Kinetic formulation
KW - Stochastic partial differential equations
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U2 - 10.1016/j.jmaa.2018.01.054
DO - 10.1016/j.jmaa.2018.01.054
M3 - Article
AN - SCOPUS:85044596054
SN - 0022-247X
VL - 461
SP - 1416
EP - 1458
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -