Kolmogorov continuity and stability of sample paths of entropy solutions of stochastic conservation laws

Author:

Bhar Suprio1,Biswas Imran H.2,Khan Saibal3,Vallet Guy4

Affiliation:

1. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur 208016, India

2. Centre for Applicable Mathematics, Tata Institute of Fundamental Research, P.O. Box 6503, GKVK Post Office, Bangalore 560065, India

3. Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Pashan, Pune 411008, India

4. LMAP UMR — CNRS 5142, Université, de Pau et des Pays de l’Adour, IPRA BP 1155, 64013 Pau Cedex, France

Abstract

This paper is concerned with sample paths and path-based properties of the entropy solution to conservation laws with stochastic forcing. We derive a series of uniform maximal-type estimates for the viscous perturbation and establish the existence of stochastic entropy solution that has Hölder continuous sample paths. This information is then carefully choreographed with Kružkov’s technique to obtain stronger continuous dependence estimates, based on the nonlinearities, for the sample paths of the solutions. Finally, convergence of sample paths is established for vanishing viscosity approximation along with an explicit rate of convergence.

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics,Analysis

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