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- Title
Energy decay estimates and infinite blow‐up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear source.
- Authors
Ma, Lingwei; Fang, Zhong Bo
- Abstract
This paper deals with the energy decay estimates and infinite blow‐up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear source term under null Dirichlet boundary condition. By constructing a new family of potential wells, together with logarithmic Sobolev inequality and perturbation energy technique, we establish sufficient conditions to guarantee the solution exists globally or occurs infinite blow‐up and derive the polynomial or exponential energy decay estimates under some appropriate conditions.
- Subjects
DAMPING (Mechanics); WAVE equation; LOGARITHMIC functions; NONLINEAR equations; QUANTUM perturbations; VISCOELASTIC materials
- Publication
Mathematical Methods in the Applied Sciences, 2018, Vol 41, Issue 7, p2639
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.4766