Open AccessNonexistence of global solutions for a class of viscoelastic wave equations
Author(s) -
Jorge A. Esquivel-Avila
Publication year - 2021
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2021134
Subject(s) - viscoelasticity , nonlinear system , class (philosophy) , energy (signal processing) , mathematics , mathematical analysis , order (exchange) , set (abstract data type) , equations of motion , wave equation , term (time) , dynamic equation , motion (physics) , physics , classical mechanics , computer science , thermodynamics , quantum mechanics , statistics , artificial intelligence , finance , economics , programming language
We consider a class of nonlinear evolution equations of second order in time, linearly damped and with a memory term. Particular cases are viscoelastic wave, Kirchhoff and Petrovsky equations. They appear in the description of the motion of deformable bodies with viscoelastic material behavior. Several articles have studied the nonexistence of global solutions of these equations due to blow-up. Most of them have considered non-positive and small positive values of the initial energy and recently some authors have analyzed these equations for any positive value of the initial energy. Within an abstract functional framework we analyze this problem and we improve the results in the literature. To this end, a new positive invariance set is introduced.