Nonlinear diffusion equations with nonlinear gradient noise
Konstantinos Dareiotis, Benjamin Gess
Abstract
We prove the existence and uniqueness of entropy solutions for nonlinear diffusion equations with nonlinear conservative gradient noise. As particular applications our results include stochastic porous media equations, as well as the one-dimensional stochastic mean curvature flow in graph form.
Topics & Concepts
MathematicsUniquenessNonlinear systemMathematical analysisMean curvature flowWasserstein metricBalanced flowEntropy (arrow of time)CurvaturePorous mediumMean curvatureStochastic differential equationFlow (mathematics)Noise (video)GraphApplied mathematicsWeak solutionDiffusionStochastic partial differential equationNonlinear Partial Differential EquationsStochastic processes and financial applicationsGeometric Analysis and Curvature Flows