Guardat en:
| Autors principals: | , , |
|---|---|
| Format: | Preprint |
| Publicat: |
2026
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/2604.26549 |
| Etiquetes: |
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- In this work, we investigate the well-posedness of a stochastic heat equation with an arbitrary (but polynomial) nonlinearity in any dimension $d\geq 1$ perturbed by a multiplicative white noise in the Stratonovich form, subject to an $L^2-$norm constraint on the solution. In bounded smooth domains, we establish the existence of a martingale solution taking values in $H_0^1 \cap L^p$ for arbitrary $2 \le p < \infty$, using a modified Faedo-Galerkin scheme. By utilizing a sequence of self-adjoint operators which are bounded in $L^p$ for any $2 \le p < \infty$, we provide a novel proof of an Itô formula for the $L^p-$norm of the solution. Together with pathwise uniqueness of the martingale solution, the Yamada-Watanabe result then yields the existence of a strong solution and uniqueness in law.