Well-posedness of nonlinear diffusion equations with nonlinear,\n conservative noise

2017/12/15 by Benjamin Fehrman, Benjamin Gess, Fehrman, Benjamin +1 · 4 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1712.05775

openalex publication_date 2017/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the pathwise well-posedness of stochastic porous media and fast\ndiffusion equations driven by nonlinear, conservative noise. As a consequence,\nthe generation of a random dynamical system is obtained. This extends results\nof the second author and Souganidis, who considered analogous spatially\nhomogeneous and first-order equations, and earlier works of Lions, Perthame,\nand Souganidis.\n

Cited by

• Ergodicity for the Dean--Kawasaki Equation with Dirichlet Boundary Conditions: Taming the Square-Root
• Fluctuating Hydrodynamics of the Ising-Kac-Kawasaki Model and Nonlinear Fluctuations Near Criticality
• Stochastic evolution equations with nonlinear diffusivity, recent progress and critical cases
• Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process

Related

• Path-by-path well-posedness of nonlinear diffusion equations with\n multiplicative noise
• Porous media equations with nonlinear gradient noise and Dirichlet boundary conditions
• Well-posedness of the obstacle problem for stochastic nonlinear diffusion equations: an entropy formulation
• Stochastic continuity equations with conservative noise
• An optimal local theory for reaction-diffusion equations driven by non-trace-class noise