Continuous dependence estimate for conservation laws with Levy noise

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:259

Article

Biswas, Imran H.¹  Koley, Ujjwal¹  Majee, Ananta K.¹ 

[1] Tata Inst Fundamental Res, Ctr Applicable Math, Bangalore 560065, Karnataka, India

关键词: Conservation laws;    Stochastic forcing;    Levy noise;    Stochastic entropy solution;    Stochastic partial differential equations;    Kruzkov's entropy;   

DOI  :  10.1016/j.jde.2015.06.024

来源: Elsevier

【 摘 要 】

We are concerned with multidimensional stochastic balance laws driven by Levy processes. Using bounded variation (BV) estimates for vanishing viscosity approximations, we derive an explicit continuous dependence estimate on the nonlinearities of the entropy solutions under the assumption that Levy noise only depends on the solution. This result is used to show the error estimate for the stochastic vanishing viscosity method. In addition, we establish fractional BV estimate for vanishing viscosity approximations in case the noise coefficient depends on both the solution and spatial variable. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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