Solution theory to semilinear hyperbolic stochastic partial differential equations with polynomially bounded coefficients. (December 2019)

• Record Type: Journal Article
• Authors: Ascanelli, Alessia; Coriasco, Sandro; Süß, André
• Is Part Of: Nonlinear analysis. Volume 189(2019)
• Publication Date: 2019-12
• Subjects: primary 35L10 60H15 -- secondary 35L40 35S30; Semilinear stochastic hyperbolic partial differential equations -- Variable coefficients -- Fourier integral operators; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111574
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We provide conditions on the initial data and on the stochastic terms, namely, on the associated spectral measure, so that mild solutions exist and are unique in suitably chosen functional classes. More precisely, function-valued solutions are obtained, as well as a regularity result.