Stochastic systems of diffusion equations with polynomial reaction terms

Article type: Research Article

Authors: Pham, Du^a | Nguyen, Phuong^{b; *}

Affiliations: [a] Department of Mathematics, University of Texas at San Antonio, One UTSA Circle San Antonio, Texas 78249, USA. E-mail: du.pham@utsa.edu | [b] The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 East Third Street, Rawles Hall, Bloomington, Indiana 47405, USA. E-mail: phunguye@indiana.edu

Correspondence: [*] Corresponding author. E-mail: phunguye@indiana.edu.

Abstract: In this work, we consider the stochastic version of the diffusion equations with polynomial reaction terms forced by a multiplicative white noise. We establish the existence and uniqueness of a maximal pathwise solution for a limited period of time. The proof relies on the Skorohod representation theorem, the Gyöngy–Krylov theorem and stopping time arguments.

Keywords: stochastic quasi-linear parabolic equations, martingale and pathwise solutions, local problems

DOI: 10.3233/ASY-161378

Journal: Asymptotic Analysis, vol. 99, no. 1-2, pp. 125-161, 2016