We consider a system of reaction–diffusion equations including chemotaxis terms and coming out of the modelling of multiple sclerosis. The global existence of strong solutions to this system in any dimension is proved, and it is also shown that the solution is bounded uniformly in time. Finally, a nonlinear stability result is obtained when the chemotaxis term is not too big. We also perform numerical simulations to show the appearance of Turing patterns when the chemotaxis term is large.

中文翻译：

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多发性硬化模型趋化系统的全局适定性和非线性稳定性

我们考虑了一个反应扩散方程系统，包括趋化性项和来自多发性硬化症的建模。证明了该系统在任何维度上强解的全局存在性，并证明了该解在时间上是一致有界的。最后，当趋化项不太大时，得到非线性稳定性结果。我们还进行数值模拟以显示当趋化项很大时图灵模式的出现。