On Nonlinear Stochastic Balance Laws

Details On Nonlinear Stochastic Balance Laws On Nonlinear Stochastic Balance Laws

2011-11-22

arxiv.org/abs/1111.5217v1

Mathematics

Analysis of PDEs

Scientific paper

We are concerned with multidimensional stochastic balance laws. We identify a class of nonlinear balance laws for which uniform spatial $BV$ bounds for vanishing viscosity approximations can be achieved. Moreover, we establish temporal equicontinuity in $L^1$ of the approximations, uniformly in the viscosity coefficient. Using these estimates, we supply a multidimensional existence theory of stochastic entropy solutions. In addition, we establish an error estimate for the stochastic viscosity method, as well as an explicit estimate for the continuous dependence of stochastic entropy solutions on the flux and random source functions. Various further generalizations of the results are discussed.

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