Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 531, Issue 1, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2023.127752
Keywords
Fractional conservation laws; Young measures; Kinetic solution; Invariant measure; Multiplicative noise; Brownian noise
Categories
Ask authors/readers for more resources
This paper considers the Cauchy problem for the nonlinear fractional conservation laws with stochastic forcing. The existence of desired kinetic solution and the convergence of the approximate viscous solutions to a kinetic solution are shown. Furthermore, the existence of an invariant measure under a nonlinearity-diffusivity condition is proved, and the uniqueness and ergodicity of the invariant measure are demonstrated.
In this paper, we consider the Cauchy problem for the nonlinear fractional con-servation laws with stochastic forcing. In particular, we are concerned with the well-posedness theory and the study of the long-time behavior of solutions for such equations. We show the existence of desired kinetic solution by using the vanish-ing viscosity method. In fact, we establish strong convergence of the approximate viscous solutions to a kinetic solution. Moreover, under a nonlinearity-diffusivity condition, we prove the existence of an invariant measure using the well-known Krylov-Bogoliubov theorem. Finally, we show the uniqueness and ergodicity of the invariant measure.(c) 2023 Elsevier Inc. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available