Friday, May 23, 2025 - 10:00 in V2-210
Stochastic nonlinear heat equation with constraints: existence of martingale solutions and pathwise uniqueness
A talk in the SPDEvent series by
Ashish Bawalia from Indian Institute of Technology Roorkee
| Abstract: |
We examine a stochastic nonlinear heat equation in any dimension $d \geq 1$ driven by a Gaussian noise in the Stratonovich form along with a constraint on the $L^2$-norm of the solution. The existence of an $H_0^1\cap L^p$-valued ($2 \leq p < \infty$) martingale solution is shown. Moreover, we have shown that this solution is invariant in a Hilbertian manifold M, in particular unit sphere, that is, if the initial data is in M, then all its corresponding trajectories stay in M. Finally, the pathwise uniqueness of the solution is proved which concludes the existence of a strong solution via a Yamada-Watanabe type result.
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