Long‐Time Behavior, Invariant Measures, and Regularizing Effects for Stochastic Scalar Conservation Laws

By Benjamin Gess, Panagiotis E. Souganidis. 2014

81 citations recorded by the source corpus.

We study the long‐time behavior and regularity of the pathwise entropy solutions to stochastic scalar conservation laws with random‐in‐time spatially homogeneous fluxes and periodic initial data. We prove that the solutions converge to their spatial average, which is the unique invariant measure of the associated random dynamical system, and provide a rate of convergence, the latter being new even in the deterministic case for dimensions higher than 2. The main tool is a new regularization result in the spirit of averaging lemmata for scalar conservation laws, which, in particular, implies a regularization by noise‐type result for pathwise quasi‐solutions.© 2016 Wiley Periodicals, Inc.

Subfields: Applied Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/c04d18c89b4ef5cea92cba04eac16c76f60708f3

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In Applied Mathematics

  1. Samy Tindel
  2. A. Deya
  3. Massimiliano Gubinelli
  4. Martina Hofmanov'a
  5. Benjamin Gess
  6. Panagiotis E. Souganidis
  7. S. Armstrong
  8. Peter K. Friz

In Control and Systems Engineering

  1. Massimiliano Gubinelli
  2. Samy Tindel
  3. Panagiotis E. Souganidis
  4. A. Deya
  5. Benjamin Gess
  6. Martina Hofmanov'a
  7. Wei Liu
  8. Bixiang Wang

In Finance

  1. Samy Tindel
  2. A. Deya
  3. Benjamin Gess
  4. Massimiliano Gubinelli
  5. Panagiotis E. Souganidis
  6. Martina Hofmanov'a
  7. Martin Hairer
  8. Peter K. Friz

Citations in the corpus