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

  • Bixiang WANG
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  • Department of Mathematics, New Mexico Institute of Mining and Technology Socorro, NM 87801, USA
Bixiang WANG, E-mail: bwang@nmt.edu

Received date: 2025-03-02

  Revised date: 2025-05-01

  Online published: 2025-11-14

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.

Cite this article

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 . DOI: 10.1007/s10473-025-0610-z

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