Han, Beom-SeokYi, Jaeyun2024-02-202024-02-202024-02-202023-10-2610.1016/j.jde.2023.10.042https://infoscience.epfl.ch/handle/20.500.14299/204443WOS:001109357600001We study the existence, uniqueness, and regularity of the solution to the stochastic reaction-diffusion equation (SRDE) with colored noise F-center dot:partial derivative(t)u = aijuxixj +biuxi + cu - b<overline>u1+beta +xi u1+gamma F-center dot, (t, x) is an element of R+ x Rd; u(0, <middle dot>) = u0,where a(ij), b(i), c, b<overline> and xi are C-2 or L-infinity bounded random coefficients. Here beta > 0 denotes the degree of strong dissipativity and gamma > 0 represents the degree of stochastic force. Under the reinforced Dalang's condition on F-center dot, we show the well-posedness of the SRDE provided gamma < kappa (beta+1) d+2 where kappa > 0 is the constant related to F-center dot. Our result assures that strong dissipativity prevents the solution from blowing up. Moreover, we provide the maximal H & ouml;lder regularity of the solution in time and space. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).Physical SciencesStochastic Partial Differential EquationStochastic Reaction-Diffusion EquationStrong DissipativitySuper-Linear, Colored NoiseLp RegularityHolder Regularitytext::journal::journal article::research article