Weakly coupled systems of semilinear effectively damped waves with time-dependent coefficient, different power nonlinearities and different regularity of the data. (October 2018)

• Record Type: Journal Article
• Authors: Mohammed Djaouti, Abdelhamid; Reissig, Michael
• Is Part Of: Nonlinear analysis. Volume 175(2018)
• Page Start: 28
• Page End: 55
• Publication Date: 2018-10
• Subjects: 35L52 -- 35L71; Weakly coupled hyperbolic systems -- Damped wave equations -- Cauchy problem -- Global existence -- L2-decay -- Effective dissipation -- Small data solutions; 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.2018.05.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the global existence of small data solutions to the Cauchy problem for semilinear damped wave equations with an effective dissipation term, where the data are supposed to belong to different classes of regularity. We apply these results to the Cauchy problem for weakly coupled systems of semilinear effectively damped waves with respect to the defined classes of regularity for different power nonlinearities.