Infinite energy solutions for critical wave equation with fractional damping in unbounded domains. (May 2016)

• Record Type: Journal Article
• Authors: Savostianov, Anton
• Is Part Of: Nonlinear analysis. Volume 136(2016)
• Page Start: 136
• Page End: 167
• Publication Date: 2016-05
• Subjects: 35B40 -- 35B45 -- 35L70; Damped wave equation -- Fractional damping -- Global attractor -- Unbounded domain -- Strichartz estimates; 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.2016.02.016
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of R 3 with fractional damping of the form ( − Δ x + 1 ) 1 2 ∂ t u . The work extends previously known results for bounded domains in finite energy case. Furthermore, well-posedness and existence of locally-compact smooth attractors for the critical quintic non-linearity are obtained under less restrictive assumptions on non-linearity, relaxing some artificial technical conditions used before. This is achieved by virtue of new type Lyapunov functional that allows to establish extra space–time regularity of solutions of Strichartz type.