Behavior of Solutions to a Fourth-Order Nonlinear Parabolic Equation with Logarithmic Nonlinearity

被引：6
|
作者：
Zhou, Jun [1 ]
机构：
[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China
来源：
APPLIED MATHEMATICS AND OPTIMIZATION | 2021年 / 84卷 / 01期
关键词：
Fourth order parabolic equation; Epitaxial growth; Global existence; Blow-up; Extinction; Exponential decay; SEMILINEAR HYPERBOLIC-EQUATIONS; GLOBAL ASYMPTOTICAL BEHAVIOR; GROUND-STATE SOLUTION; THIN-FILM EQUATION; BLOW-UP; POTENTIAL WELLS; EXISTENCE; NONEXISTENCE; INSTABILITY; THEOREMS;
D O I：
10.1007/s00245-019-09642-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with a class of fourth-order parabolic equations modeling the evolution of the epitaxial growth of nanoscale thin films. By exploiting the variational structure of the equation, the logarithmic Sobolev inequality and a family of potential wells, the conditions on existence of global and infinite time blow-up solutions are obtained. Moreover, the finite time extinction and exponential decay of the solutions are also discussed.
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页码：191 / 225
页数：35
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