Joint work with Ekaterina T. Kolkovska.
We study a semilinear partial differential equation defined on a bounded domain with Dirichlet boundary conditions, perturbed by a noise term that depends on the gradient of the solution. Using the method of stochastic characteristics, we establish the existence and uniqueness of a strong solution in suitable regularity spaces, and derive necessary and sufficient conditions for nonglobal existence given in terms of the Osgood condition for the reaction term. In the case of finite-time blowup, we provide quantitative bounds for the explosion time and upper estimates for the probability of finite time blowup. In the deterministic setting, we obtain explicit upper and lower bounds for the blowup time when the coefficient of the linear term is large. Our analysis is based on the associated stochastic flow and shows that, with high probability, the random perturbation prevents finite-time blowup when the initial condition is sufficiently small.
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| Subject : | : | Talk |
| Topics | : | Probability Theory |
| PDF version | : |  PDF version |
