On Nonlinear Stochastic Balance Laws

By Gui-Qiang G. Chen, Qian Ding, Kenneth Hvistendahl Karlsen. 2011

108 citations recorded by the source corpus.

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 L1 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.

Subfields: Applied Mathematics, Computational Mechanics, Finance

View Paper: https://www.semanticscholar.org/paper/8d50bbeeacc330f12aadc8d3c3b25607dc19f2fb

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In Applied Mathematics

1. Martina Hofmanov'a
2. Benjamin Gess
3. Panagiotis E. Souganidis
4. Massimiliano Gubinelli
5. Samy Tindel
6. A. Deya
7. Caroline Bauzet
8. Petra Wittbold

In Computational Mechanics

1. Benjamin Gess
2. Panagiotis E. Souganidis
3. Martina Hofmanov'a
4. Caroline Bauzet
5. Petra Wittbold
6. Guy Vallet
7. Arnaud Debussche
8. Massimiliano Gubinelli

In Finance

1. Benjamin Gess
2. Panagiotis E. Souganidis
3. Martina Hofmanov'a
4. Samy Tindel
5. A. Deya
6. Massimiliano Gubinelli
7. Caroline Bauzet
8. Petra Wittbold

Citations in the corpus

• A priori estimates for rough PDEs with application to rough conservation laws (2016, background): “where the Itô stochastic forcing is driven by a finite- or infinite-dimensional Wiener process (see [2, 9, 14, 12, 13, 20, 40, 42, 45, 58, 60]).”
• Long‐Time Behavior, Invariant Measures, and Regularizing Effects for Stochastic Scalar Conservation Laws (2014, background): “The case of multiplicative semilinear noise dependence in Itô’s form, that is stochastic PDE (SPDE for short) of the form (1.11) du+ divA(u)dt = g(u)dWt, where W denotes a possibly infinite dimensional Wiener process, has attracted considerable interest in recent years; see for example, Bauzet, Val”
• Scalar conservation laws with stochastic forcing (2010, result): “ stochastic forcing” published in the Journal of Functional Analysis, 259 (2010), pp. 1014-1042. Since the publication of this paper, other articles on this subject have appeared. Chen, Ding, Karlsen [CDK12] and Bauzet, Vallet and Wittbolt [BVW12] have generalized the Kruzkov approach to the stochas”
• THE CAUCHY PROBLEM FOR CONSERVATION LAWS WITH A MULTIPLICATIVE STOCHASTIC PERTURBATION (2012, background): “In the recent paper [4], Chen, Ding and Karlsen propose to revisit the work of Feng and Nualart.”
• The Dirichlet problem for a conservation law with a multiplicative stochastic perturbation (2014, background): “In the recent paper [4], Chen, Ding and Karlsen propose to revisit the work of Feng and Nualart.”