On a Stochastic First Order Hyperbolic Equation in a Bounded Domain

@inproceedings{Vallet2009OnAS,
  title={On a Stochastic First Order Hyperbolic Equation in a Bounded Domain},
  author={Guy Vallet and Petra Wittbold},
  year={2009}
}
In this paper, we are interested in the stochastic perturbation of a first order hyperbolic equation of nonlinear type. In order to illustrate our purposes, we have chosen a scalar conservation law in a bounded domain with homogeneous Dirichlet condition on the boundary. Using the concept of measure-valued solutions and Kruzhkov’s entropy formulation, a result of existence and uniqueness of the entropy solution is given. keywords : Stochastic PDE, first-order hyperbolic problems, bounded domain… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 30 references

Panov

E. Yu
Existence of strong traces for generalized solutions of multidimensional scalar conservation laws. J. Hyperbolic Diff. Equ., 2(4):885–908 • 2005
View 3 Excerpts
Highly Influenced

Stochastic evolution equations : A Hilbert space approach

W. Grecksch, C. Tudor
volume 85 of Mathematical Research. Akademie-Verlag, Berlin • 1995
View 3 Excerpts
Highly Influenced

Valadier. Young measures on topological spaces with applications in control theory and probability theory, volume 571 of Mathematics and its Applications

Ch. Castaing, P. Raynaud de Fitte
2004
View 1 Excerpt

On a stochastic scalar conservation law

J. U. Kim
Indiana Univ. Math. J., 52(1):227–256 • 2003
View 2 Excerpts

Renormalized entropy solutions of scalar conservation laws with boundary condition

J. Carrillo, P. Wittbold
J. Differ. Equ., 185(1):137–160 • 2002
View 2 Excerpts

Strong traces for solutions of multidimensional scalar conservation laws

A. Vasseur
Arch. Ration. Mech. Anal., 160(3):181–193 • 2001
View 1 Excerpt

Dirichlet problem for a nonlinear conservation law

G. Vallet
Rev. Mat. Complut., 13(1):231–250 • 2000
View 2 Excerpts

Stochastic perturbation of nonlinear degenerate parabolic problems

G. Vallet.
2000

and Ya

E. Weinan, K. Khanin, A. Mazel
Sinai. Invariant measures for Burgers equation with stochastic forcing. Ann. Math. (2), 151(3):877–960 • 2000
View 1 Excerpt

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