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.

引用

页码：191 / 225

页数：35

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