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Article Dans Une Revue Journal of Hyperbolic Differential Equations Année : 2023

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

Suprio Bhar
  • Fonction : Auteur
Imran Biswas
  • Fonction : Auteur
Saibal Khan
  • Fonction : Auteur

Résumé

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.
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Dates et versions

hal-04312922 , version 1 (28-11-2023)

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Citer

Suprio Bhar, Imran Biswas, Saibal Khan, Guy Vallet. Kolmogorov continuity and stability of sample paths of entropy solutions of stochastic conservation laws. Journal of Hyperbolic Differential Equations, 2023, 20 (02), pp.277-348. ⟨10.1142/S0219891623500091⟩. ⟨hal-04312922⟩
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