Nonlinear diffusion equations with nonlinear gradient noise

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.

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References in corpus (7)

• Degenerate parabolic stochastic partial differential equations: Quasilinear case
• On L_p- theory for stochastic parabolic integro-differential equations
• Multi-valued, singular stochastic evolution inclusions
• Entropy solutions for stochastic porous media equations
• Entropic and gradient flow formulations for nonlinear diffusion
• Supremum estimates for degenerate, quasilinear stochastic partial differential equations
• On the boundedness of solutions of SPDEs

Cited by in corpus (5)

• Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise
• Weak error analysis for a nonlinear SPDE approximation of the Dean-Kawasaki equation
• Well-posedness of Dean-Kawasaki Equation with Singular Interactions
• Weak Error of Dean-Kawasaki Equation with Smooth Mean-Field Interactions
• Well-Posedness of the generalised Dean-Kawasaki Equation with correlated noise on bounded domains