Hyperbolic and parabolic equations with several opposite-sign source at critical initial energy level in heat and vibrating systems. (June 2020)

• Record Type: Journal Article
• Authors: Dai, Xiaoqiang
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 35L70 -- 35K57; Heat and vibrating system -- Critical initial data -- Asymptotic behavior -- Global nonexistence; 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.2020.111752
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study semilinear hyperbolic equations and parabolic equations with several opposite sign source terms under the Dirichlet boundary condition in heat and vibrating systems. For the above problems, we prove the global nonexistence of solution and give the sharp conditions at critical energy level. Furthermore, we prove that the existence of global solution of parabolic equation vanishes to zero as time goes to infinity, which is different from the behavior of solution of the hyperbolic equation.