一类非线性四阶抛物型方程解的存在性  

Existence of Solutions for a Class of Nonlinear Fourth-Order Parabolic Equations

作　　者：李彬 朱永政[1] 

机构地区：[1]大连交通大学理学院,辽宁 大连

出　　处：《理论数学》2023年第9期2633-2638,共6页Pure Mathematics

摘　　要：以一般的线性抛物型方程为背景,引入了一类非线性的四阶抛物型方程。本文主要研究该方程弱解的存在性问题。在方法上,结合Galerkin理论和能量估计方法。通过构造逼近解、对逼近解作估计、对逼近解取极限得到这类方程弱解的存在性。Taking the general linear parabolic equations as background, a class of nonlinear fourth-order parabolic equations is introduced. In this paper, we mainly study the existence of weak solutions to this equation. In the method, Galerkin theory and energy estimation method are combined. The existence of the weak solution of this kind of equation is obtained by constructing the approxima-tion solution, estimating the approximation solution and taking the limit of the approximation so-lution.

关 键 词：非线性抛物型方程 Galerkin理论 存在性 

分 类 号：O17[理学—数学]