TY - JOUR
T1 - Viscous scalar conservation law with stochastic forcing
T2 - strong solution and invariant measure
AU - Martel, Sofiane
AU - Reygner, Julien
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020/6/1
Y1 - 2020/6/1
N2 - We are interested in viscous scalar conservation laws with a white-in-time but spatially correlated stochastic forcing. The equation is assumed to be one-dimensional and periodic in the space variable, and its flux function to be locally Lipschitz continuous and have at most polynomial growth. Neither the flux nor the noise need to be non-degenerate. In a first part, we show the existence and uniqueness of a global solution in a strong sense. In a second part, we establish the existence and uniqueness of an invariant measure for this strong solution.
AB - We are interested in viscous scalar conservation laws with a white-in-time but spatially correlated stochastic forcing. The equation is assumed to be one-dimensional and periodic in the space variable, and its flux function to be locally Lipschitz continuous and have at most polynomial growth. Neither the flux nor the noise need to be non-degenerate. In a first part, we show the existence and uniqueness of a global solution in a strong sense. In a second part, we establish the existence and uniqueness of an invariant measure for this strong solution.
KW - Invariant measure
KW - Stochastic conservation laws
UR - https://www.scopus.com/pages/publications/85085324411
U2 - 10.1007/s00030-020-00637-9
DO - 10.1007/s00030-020-00637-9
M3 - Article
AN - SCOPUS:85085324411
SN - 1021-9722
VL - 27
JO - Nonlinear Differential Equations and Applications
JF - Nonlinear Differential Equations and Applications
IS - 3
M1 - 34
ER -