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Energy decay estimates and infinite blow‐up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear source
Author(s) -
Ma Lingwei,
Fang Zhong Bo
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4766
Subject(s) - mathematics , logarithm , mathematical analysis , wave equation , nonlinear system , exponential decay , sobolev space , dirichlet boundary condition , exponential function , perturbation (astronomy) , energy (signal processing) , boundary value problem , exponential growth , physics , statistics , quantum mechanics , nuclear physics
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.