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
DOI: 10.12677/PM.2023.139269, PDF,   
作者: 李 彬, 朱永政：大连交通大学理学院，辽宁 大连
关键词: 非线性抛物型方程；Galerkin理论；存在性；Nonlinear Parabolic Equations； Galerkin Theory； Existence
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。
Abstract: 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.
文章引用：李彬, 朱永政. 一类非线性四阶抛物型方程解的存在性[J]. 理论数学, 2023, 13(9): 2633-2638. https://doi.org/10.12677/PM.2023.139269

参考文献

[1] Zangwill, A. (1996) Some Causes and a Consequence of Epitaxial Roughening. Journal of Crystal Growth, 163, 8-21. [Google Scholar] [CrossRef] 
[2] Ortiz, M., Repetto, E.A. and Si, H. (1999) A Continuum Model of Kinetic Roughening and Coarsening in Thin Films. Journal of the Mechanics & Physics of Solids, 47, 697-730. [Google Scholar] [CrossRef] 
[3] Bb, K., Stein, O. and Winkler, M. (2003) A Fourth-Order Parabolic Equation Modeling Epitaxial Thin Film Growth. Journal of Mathematical Analysis and Applications, 286, 459-490. [Google Scholar] [CrossRef] 
[4] Xu, R., Chen, T., Liu, C., et al. (2015) Global Well-Posedness and Global Attractor of Fourth Order Semilinear Parabolic Equation. Mathematical Methods in the Applied Sciences, 38, 1515-1529. [Google Scholar] [CrossRef] 
[5] Liu, C. (2008) A Fourth Order Parabolic Equation with Nonlinear Principal Part. Nonlinear Analysis Theory Methods & Applications, 68, 393-401. [Google Scholar] [CrossRef] 
[6] Liang, B., Ji, R. and Zhu, Y. (2012) Positive Solutions to a Nonlinear Fourth-Order Partial Differential Equation. Nonlinear Analysis: Real World Applications, 13, 2853-2862. [Google Scholar] [CrossRef] 
[7] Adams, R.A. (1975) Sobolev Spaces. Academic Press, New York.
[8] Simon, J. (1986) Compact Sets in the Space L p (0, T; B). Annali Di Matematica Pura Ed Applicata, 146, 65-96. [Google Scholar] [CrossRef] 

为你推荐