| Abstract: |
| This talk is based on joint work with Sandra Cerrai and Gianmario Tessitore.
We present well-posedness and small-noise asymptotic results for a class of stochastic
reaction-diffusion equations on bounded domains, driven by nonlinear and temporally nonlocal
multiplicative noise. The diffusion coefficient depends on the solution through a conditional
expectation at the final time, while the reaction term is only assumed to be continuous and
quasi-dissipative, with no growth bounds or local Lipschitz assumptions. To handle these
difficulties, we avoid relying on the theory of infinite-dimensional quasilinear PDEs and instead
work directly at the SPDE level, combining a mild formulation with a Salins-type solution map
and contraction arguments. This yields existence and uniqueness for sufficiently small noise, as
well as a large deviation principle for the laws of the solution trajectories. |
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