On Nonlinear Stochastic Balance Laws

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• 作者：Gui-Qiang Chen (123) chengq@maths.ox.ac.uk
  Qian Ding (3) dingqian@math.northwestern.edu
  Kenneth H. Karlsen (4) kennethk@math.uio.no
• 刊名：Archive for Rational Mechanics and Analysis
• 出版年：2012
• 出版时间：June 2012
• 年：2012
• 卷：204
• 期：3
• 页码：707-743
• 全文大小：370.5 KB
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• 作者单位：1. Mathematical Institute, University of Oxford, 24鈥?9 St. Giles, Oxford, OX1 3LB UK2. School of Mathematical Sciences, Fudan University, Shanghai, 200433 China3. Department of Mathematics, Northwestern University, Evanston, IL 60208-2730, USA4. Centre of Mathematics for Applications, University of Oslo, P. O. Box 1053, Blindern, 0316 Oslo, Norway
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Electromagnetism, Optics and Lasers
  Mathematical and Computational Physics
  Complexity
  Fluids
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0673

文摘

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.