[HTML][HTML] Entropy solutions for stochastic porous media equations
We provide an entropy formulation for porous medium-type equations with a stochastic, non-
linear, spatially inhomogeneous forcing. Well-posedness and L 1-contraction is obtained in …
linear, spatially inhomogeneous forcing. Well-posedness and L 1-contraction is obtained in …
Convergence of approximations to stochastic scalar conservation laws
S Dotti, J Vovelle - Archive for Rational Mechanics and Analysis, 2018 - Springer
We develop a general framework for the analysis of approximations to stochastic scalar
conservation laws. Our aim is to prove, under minimal consistency properties and bounds …
conservation laws. Our aim is to prove, under minimal consistency properties and bounds …
[HTML][HTML] The Cauchy problem for fractional conservation laws driven by Lévy noise
N Bhauryal, U Koley, G Vallet - Stochastic Processes and their applications, 2020 - Elsevier
In this article, we explore some of the main mathematical problems connected to
multidimensional fractional conservation laws driven by Lévy processes. Making use of an …
multidimensional fractional conservation laws driven by Lévy processes. Making use of an …
Convergence of an operator splitting scheme for fractional conservation laws with Levy noise
SR Behera, AK Majee - Computational Methods in Applied …, 2024 - degruyter.com
In this paper, we are concerned with an operator-splitting scheme for linear fractional and
fractional degenerate stochastic conservation laws driven by multiplicative Lévy noise. More …
fractional degenerate stochastic conservation laws driven by multiplicative Lévy noise. More …
Analysis of a splitting method for stochastic balance laws
KH Karlsen, EB Storrøsten - IMA Journal of Numerical Analysis, 2018 - academic.oup.com
We analyse a semidiscrete splitting method for conservation laws driven by a semilinear
noise term. Making use of fractional bounded variation (BV) estimates, we show that the …
noise term. Making use of fractional bounded variation (BV) estimates, we show that the …
Homogeneous Dirichlet problem for degenerate parabolic-hyperbolic PDE driven by Lévy noise
SR Behera, AK Majee - arXiv preprint arXiv:2408.13530, 2024 - arxiv.org
In this article, we study the homogeneous Dirichlet problem for a degenerate parabolic-
hyperbolic PDE perturbed by Levy noise. In particular, we develop the well-posedness …
hyperbolic PDE perturbed by Levy noise. In particular, we develop the well-posedness …
Convergence of the finite volume method for scalar conservation laws with multiplicative noise: an approach by kinetic formulation
S Dotti, J Vovelle - Stochastics and Partial Differential Equations: Analysis …, 2020 - Springer
Under a standard CFL condition, we prove the convergence of the explicit-in-time Finite
Volume method with monotone fluxes for the approximation of scalar first-order conservation …
Volume method with monotone fluxes for the approximation of scalar first-order conservation …
Existence and uniqueness result for an hyperbolic scalar conservation law with a stochastic force using a finite volume approximation
C Bauzet, V Castel, J Charrier - Journal of Hyperbolic Differential …, 2020 - World Scientific
We are interested in multi-dimensional nonlinear scalar conservation laws forced by a
multiplicative stochastic noise with a general time and space dependent flux-function. We …
multiplicative stochastic noise with a general time and space dependent flux-function. We …
Nonlinear anisotropic degenerate parabolic-hyperbolic equations with stochastic forcing
GQG Chen, PHC Pang - Journal of Functional Analysis, 2021 - Elsevier
We are concerned with nonlinear anisotropic degenerate parabolic-hyperbolic equations
with stochastic forcing, which are heterogeneous (ie, not space-translational invariant). A …
with stochastic forcing, which are heterogeneous (ie, not space-translational invariant). A …
Invariant measures for nonlinear conservation laws driven by stochastic forcing
GQG Chen, PHC Pang - Chinese Annals of Mathematics, Series B, 2019 - Springer
Some recent developments in the analysis of long-time behaviors of stochastic solutions of
nonlinear conservation laws driven by stochastic forcing are surveyed. The existence and …
nonlinear conservation laws driven by stochastic forcing are surveyed. The existence and …