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On Nonlinear Stochastic Balance Laws |
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| Authors: | Gui-Qiang Chen Qian Ding Kenneth H. Karlsen |
| Affiliation: | 1. Mathematical Institute, University of Oxford, 24–29 St. Giles, Oxford, OX1 3LB, UK 2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China 3. Department of Mathematics, Northwestern University, Evanston, IL, 60208-2730, USA 4. Centre of Mathematics for Applications, University of Oslo, P. O. Box 1053, Blindern, 0316, Oslo, Norway |
| Abstract: | We are concerned with multidimensional stochastic balance laws. We identify a class of nonlinear balance laws for which uniform spatial BV bound 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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