外延薄膜生长方程全局弱解的渐近行为

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2024-09-07 DOI:10.1016/j.nonrwa.2024.104209

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引用次数: 0

摘要

本文关注的是涉及梯度型对数非线性和吸收项的外延薄膜生长方程的 Dirichlet 初始边界值问题。通过引入等效规范和近似 Lipschitz 函数，结合 Faedo-Galerkin 近似技术和势阱族，我们建立了全局弱解的好求解性。同时，我们利用能量函数和相关的内哈里流形对所考虑问题的衰减特性和增长现象进行了分类。

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Asymptotic behaviors of global weak solutions for an epitaxial thin film growth equation

This paper is concerned with the Dirichlet initial boundary value problem of an epitaxial thin film growth equation involving gradient-type logarithmic nonlinearity and absorption terms. By introducing an equivalent norm and approximating Lipschitz functions, combining with the technique of Faedo–Galerkin approximation and the family of potential wells, we establish the well-posedness of global weak solutions. Meantime, we classify the decay properties and grow-up phenomenon of the considered problem by using the energy functional and the related Nehari manifold.

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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.