In this paper we consider a class of stochastic reaction-diffusion equations. We provide local
well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of …

In this paper, we investigate the global well-posedness of reaction-diffusion systems with
transport noise on the-dimensional torus. We show new global well-posedness results for a …

We prove global well-posedness for a class of dissipative semilinear stochastic evolution
equations with singular drift and multiplicative Wiener noise. In particular, the nonlinear term …

A condition is identified that implies that solutions to the stochastic reaction-diffusion
equation∂ u∂ t= A u+ f (u)+ σ (u) W˙ on a bounded spatial domain never explode. We …

We study the existence, uniqueness, and regularity of the solution to the stochastic reaction-
diffusion equation (SRDE) with colored noise F˙:∂ tu= aijuxix j+ biux i+ cu− b¯ u 1+ β+ ξ u …

We prove well-posedness for doubly nonlinear parabolic stochastic partial differential
equations of the form d X t− div γ (∇ X t) d t+ β (X t) dt∋ B (t, X t) d W t, where γ and β are the …

In this survey, we provide an in-depth exposition of our recent results on the well-posedness
theory for stochastic evolution equations, employing maximal regularity techniques. The …

In this paper, we investigate the global well-posedness of reaction-diffusion systems with
transport noise on the d-dimensional torus. We show new global well-posedness results for …

We establish well-posedness in the mild sense for a class of stochastic semilinear evolution
equations on $ L^ p $ spaces on bounded domains of $\mathbb {R}^ n $ with a nonlinear …

We study the existence, uniqueness, and regularity of the solution to the stochastic reaction-
diffusion equation (SRDE) with colored noise $\dot {F} $: $$\partial_t u= a^{ij} u_ {x^ ix^ j}+ …