带有强阻尼项的拟线性抛物方程整体解的存在性与指数增长  

Global Existence and Exponential Growth of Solution for a Quasilinear Parabolic Equation with Strong Damping

作　　者：吴娇 杨晗[1] WU Jiao;YANG Han(School of Mathematics,Southuest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,四川成都611756

出　　处：《应用数学》2021年第3期600-610,共11页Mathematica Applicata

基　　金：国家自然科学基金(11701477,11971394)。

摘　　要：本文研究拟线性项与源项的竞争对具有强阻尼项的拟线性抛物方程解的影响.利用Galerkin方法给出局部解的存在性,结合势井方法和修改的能量泛函,在不同条件下证明整体解的存在性,并估计整体解的能量衰减.最后在初始能量为负或初始能量有一临界的正的下界,且时间t趋于无穷时,解的Lp范数将以指数形式增长.In this paper,the quasilinear parabolic equation with strong damping and nonlinear source term is considered.The existence of local weak solution is proved with the help of the Galerkin method.Also,by virtue of the potential well theory and modified energy function,it is proved that the solution globally exists and which is exponential decay in the energy space.Furthermore,it is shown that the solution with Lp-norm will grow up as an exponential rate as time goes to infinity,provided the initial energy is negative or the initial energy has a critical positive lower bound.

关 键 词：拟线性抛物方程 强阻尼项 整体解 指数增长 

分 类 号：O175.26[理学—数学]