报告题目：Martingale solutions to a stochastic Keller-Segel system with nonlocal source and super-linear noise

报告人：李浅 辽宁大学

报告时间：2026年06月28日10:20-10:50

报告地点：腾讯会议ID：609-2797-9994

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校内联系人：徐佳宁 [email protected]

报告摘要：

    Global nonnegative martingale solutions are shown to exist for a stochastic Keller–Segel system with a nonlocal Fisher–KPP source and super-linear multiplicative noise. The result is obtained for nonnegative initial data with no smallness assumption, provided that the nonlocal source term is dominant. The main difficulty stems from the absence of a coercive structure and the super-linear nature of the noise. An additional cut-off with finite $L^2 $ norm in the classical Galerkin method is added to establish a well-posed approximation problem. Moreover, due to the nonlocal Fisher-KPP structure, it is necessary to prove the positivity of the approximating solution in order to obtain uniform estimates.

    In the compactness arguments, the usual tightness argument in the framework of Hilbert spaces cannot be directly applied to the uniform estimates obtained in this paper. As a result, we develop a more general version of the compactness argument and tightness criterion, which will be applied throughout the paper. This allows for the global existence of nonnegative martingale solutions to be derived from Jakubowski's version of the Skorokhod Theorem, along with a thorough discussion of the convergence properties.