数学
对数
类型(生物学)
拉普拉斯算子
非线性系统
数学分析
p-拉普拉斯算子
应用数学
物理
量子力学
生态学
生物
边值问题
出处
期刊:Filomat
[National Library of Serbia]
日期:2023-01-01
卷期号:37 (16): 5485-5507
摘要
This work is deal with a problem of wave equation with p-Laplacian, strong damping and logarithmic source terms under initial-boundary conditions. The global existence of weak solution was proved for related to the equation. Global existence results of solutions are obtained using the potential well method, Galerkin method and compactness approach corresponding to the logarithmic source term. Besides, we established the energy functional decaying polynomially to zero as the time goes to infinity due to Nakao?s inequality and some precise priori estimates on logarithmic nonlinearity. For suitable conditions we proved the finite time blow up results of solutions. The proof is based on the concavity method, perturbation energy method and differential-integral inequality technique. Additionally, under suitable assumptions on initial data, the infinite time blow up result is investigated with negative initial energy.
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