Entropy (May 2018)

Stochastic Entropy Solutions for Stochastic Nonlinear Transport Equations

  • Rongrong Tian,
  • Yanbin Tang

DOI
https://doi.org/10.3390/e20060395
Journal volume & issue
Vol. 20, no. 6
p. 395

Abstract

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This paper considers the existence and uniqueness of stochastic entropy solution for a nonlinear transport equation with a stochastic perturbation. The uniqueness is based on the doubling variable method. For the existence, we develop a new scheme of parabolic approximation motivated by the method of vanishing viscosity given by Feng and Nualart (J. Funct. Anal. 2008, 255, 313–373). Furthermore, we prove the continuous dependence of stochastic strong entropy solutions on the coefficient b and the nonlinear function f.

Keywords