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| 摘要: |
| 本文研究一类具有强阻尼和对数非线性源项的p-Laplacian型波动方程的初边值问题.使用Galerkin方法,借助对数Sobolev不等式,势阱理论和Sobolev嵌入定理,证明了弱解的整体存在唯一性,得到了爆破的最佳条件和能量以多项式衰减的估计,推广了p=2情形的结果. |
| 关键词: Galerkin方法 势阱理论 整体解 爆破 能量衰减估计 |
| DOI： |
| 分类号:O175.29 |
| 基金项目:中央高校基本科研业务费专项资金资助(2682023ZTPY013). |
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| GLOBAL EXISTENCE AND BLOW-UP FOR WAVE EQUATION OF P-LAPLACIAN TYPE WITH STRONG DAMPING AND LOGARITHMIC NON-LINEAR SOURCES |
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JIANG Rong,WANG Fan
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| Abstract: |
| In this paper, we study the initial boundary value problem of a class of p-Laplacian wave equations with strong damping and logarithmic nonlinear source terms. By means of Galerkin method, Logarithmic Sobolev inequality, potential well theory and Sobolev embedding theorem, we prove the uniqueness of the global existence of the weak solution, obtain the optimal conditions for blow-up and the estimation of the energy decay by polynomial of weak solutions, which generalize the results for the case of p = 2. |
| Key words: Galerkin method potential well theory global solution blow-up energy decay estimates |
