MARTINGALE SOLUTIONS OF FRACTIONAL STOCHASTIC REACTION-DIFFUSION EQUATIONS DRIVEN BY SUPERLINEAR NOISE

doi:10.1007/s10473-025-0610-z

Abstract

Abstract: In this paper, we prove the existence of martingale solutions of a class of stochas-tic equations with a monotone drift of polynomial growth of arbitrary order and a continuous di_usion term with superlinear growth. Both the nonlinear drift and di_usion terms are not required to be locally Lipschitz continuous. We then apply the abstract result to establish the existence of martingale solutions of the fractional stochastic reaction-di_usion equation with polynomial drift driven by a superlinear noise. The pseudo-monotonicity techniques and the Skorokhod-Jakubowski representation theorem in a topological space are used to pass to the limit of a sequence of approximate solutions de_ned by the Galerkin method.

Key words: Martingale solution, pseudo-monotonicity, superlinear noise, Skorokhod-Jakubowski theorem, fractional equation, stochastic reaction-di_usion equation

CLC Number:

60F10

Bixiang WANG. MARTINGALE SOLUTIONS OF FRACTIONAL STOCHASTIC REACTION-DIFFUSION EQUATIONS DRIVEN BY SUPERLINEAR NOISE[J].Acta mathematica scientia,Series B, 2025, 45(6): 2549-2578.

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