%0 Conference Paper %1 hyp16-bk %A Barth, Andrea %A Kröker, Ilja %B Theory, Numerics and Applications of Hyperbolic Problems I %C Cham %D 2018 %E Klingenberg, Christian %E Westdickenberg, Michael %I Springer International Publishing %K %P 125--135 %T Finite Volume Methods for Hyperbolic Partial Differential Equations with Spatial Noise %X Various real-world applications require the consideration of the influence of uncertain parameters on the solution to some nonlinear hyperbolic problem. The topic of this paper is to study the solution to a nonlinear hyperbolic PDE perturbed by a spatial noise term. In the first part of this paper, a definition of the corresponding stochastic entropy solution is defined and the required properties for the existence and uniqueness of the defined solution are discussed. The second part is devoted to numerical simulation. An approximation of the spatial noise is introduced. Further, the influence of the noise on the solution to the nonlinear hyperbolic problems is investigated. Several nonlinear numerical examples illustrate the discussion. %@ 978-3-319-91545-6

@inproceedings{hyp16-bk, abstract = {Various real-world applications require the consideration of the influence of uncertain parameters on the solution to some nonlinear hyperbolic problem. The topic of this paper is to study the solution to a nonlinear hyperbolic PDE perturbed by a spatial noise term. In the first part of this paper, a definition of the corresponding stochastic entropy solution is defined and the required properties for the existence and uniqueness of the defined solution are discussed. The second part is devoted to numerical simulation. An approximation of the spatial noise is introduced. Further, the influence of the noise on the solution to the nonlinear hyperbolic problems is investigated. Several nonlinear numerical examples illustrate the discussion.}, added-at = {2023-12-01T15:28:28.000+0100}, address = {Cham}, author = {Barth, Andrea and Kr{\"o}ker, Ilja}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2f2e653da940c1c8f666143c888a472f2/abarth}, booktitle = {Theory, Numerics and Applications of Hyperbolic Problems I}, editor = {Klingenberg, Christian and Westdickenberg, Michael}, interhash = {a8f78782783e6ca07feb59f6b697618d}, intrahash = {f2e653da940c1c8f666143c888a472f2}, isbn = {978-3-319-91545-6}, keywords = {}, pages = {125--135}, publisher = {Springer International Publishing}, timestamp = {2023-12-01T14:28:28.000+0100}, title = {Finite Volume Methods for Hyperbolic Partial Differential Equations with Spatial Noise}, year = 2018 }