Global solutions and exponential decay to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping and nonlinear logarithmic source term

• Main Authors: S.M.S. Cordeiro, D.C. Pereira, J. Ferreira, C.A. Raposo
• Format: Article
• Language: English
• Published: Elsevier 2021-06-01
• Series: Partial Differential Equations in Applied Mathematics
• Subjects: Klein–Gordon equation; Global weak solution; Asymptotic behavior; Logarithmic source term
• Online Access: http://www.sciencedirect.com/science/article/pii/S2666818120300188
• ISSN: 2666-8181

This paper is concerned with the existence and exponential stability of the global solution to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping −Δutand logarithmic source term uln|u|R2. We apply the potential well corresponding to the logarithmic nonlinearity. We prove the global weak solutions and the exponential stability for initial data in the set of stability created from the Nehari Manifold.