Global existence of martingale solutions to stochastic keller-segel system with degenerate diffusion

2025/02/27 by Jinhuan Wang, Qian Li, Wang, Jinhuan +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2502.20042

openalex publication_date 2025/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the stochastic degenerate Keller-Segel system perturbed by linear multiplicative noise in a bounded domain O. We establish the global existence of martingale solutions for this model with any nonnegative initial data in H₂^-1(O). The main challenge in proving the existence of solutions arises from the degeneracy of the porous media diffusion and the lack of coercivity in the nonlinear chemotactic term. To overcome these difficulties, we construct a solution operator and apply the Schauder fixed point theorem within the variational framework.

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