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math.AP2022
Reaction-diffusion equations with transport noise and critical superlinear diffusion: local well-posedness and positivity
Antonio Agresti, Mark Veraar
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 nov…
math.PR2022
The critical variational setting for stochastic evolution equations
Antonio Agresti, Mark Veraar
In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi- or semi-linear type. Our results improve many of the abstract res…
math.PR2022
Higher order moments for SPDE with monotone nonlinearities
Manuel V. Gnann, Jochem Hoogendijk, Mark C. Veraar
This paper introduces a new -dependent coercivity condition through which -moments for solutions can be obtained for a large class of SPDEs in the variational framework. If…