报告题目：Stochastic nonlinear heat equation with constraints: existence ofmartingale solutions and pathwise uniqueness

报告人：Zdzislaw Brzezniak, 约克大学

报告时间：5月27日 周三 上午 10:30-11:30

报告地点：数院新楼308

摘要：In my talk I reported about results from my recent two papers, almost finished, coauthored by A. Bawalia and M. Mohan. The model is a certain reaction-diffusion equations with an arbitrary (but polynomial) growth. constrained by the condition that the L2-norm of the solution is equal to one. In [1] we conspire a purely deterministic version of the problem and prove the global existence of solution and study some of the asymptotic, as → ∞, of solutions. In [1] we conspire a purely deterministic version of the problem and prove the global existence of solution and the large deviations principle. These results generalise some papers of the speaker with J. Hussain, see e.g. [3], where similar questions we studied with an arbitrary growth in dimensions d = 2, but only growth of order ≤ 6 in dimensions d = 3.

References：

[1] A. Bawalia, Z. Brze´zniak and M.T. Mohan, Global well-posedness and asymptotic analysis of a nonlinear heat equation with constraints of finite codimension. https://arxiv.org/pdf/2507.00160

[2] A. Bawalia, Z. Brze´zniak and M.T. Mohan, Global well-posedness of a stochastic nonlinear heat equation with constraints of finite codimension. https://arxiv.org/pdf/2604.26549

[3] Z. Brze´zniak and J. Hussain, Global solution of nonlinear stochastic heat equation with solutions in a Hilbert manifold, Stochastic Dynamics 20 (2020), no. 6, 2040012, 29 pp