2024/01/31 by Erika Hausenblas, Hausenblas, Erika, B. Jidjou Moghomye +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2401.17668
openalex publication_date 2024/01/31 · openalex created_date 2024/02/02 · openalex updated_date 2026/07/28
The purpose of the paper is twofold. Firstly, we want to present a Meta Theorem to show the existence of a martingale solution for coupled systems of non-linear stochastic differential equations. The idea is first to split the system by rewriting the non-linear part in a linear part acting on a given process ξ. This is done in such a way that the fixpoint with respect to ξ would be the solution. However, to show the well posedness of the \sl linearized system, one needs a cut-off argument. Under which conditions one can handle the limits of the cut-off parameter to get in the end a martingale solution of the original system is given in the Meta-Theorem. Secondly, we want to verify the full applicability of the Meta Theorem by showing the existence of a martingale solution of a highly nonlinear chemotaxis system with underlying fluid dynamic.