A class of fourth-order nonlinear parabolic equations modeling the epitaxial growth of thin films-Reference-Cited by-同舟云学术

A class of fourth-order nonlinear parabolic equations modeling the epitaxial growth of thin films

Published:2021 Issue:12 Volume:14 Page:4367
ISSN:1937-1632
Container-title:Discrete & Continuous Dynamical Systems - S
language:
Short-container-title:DCDS-S

Author:

Liu Yang,Li Wenke

Abstract

<p style='text-indent:20px;'>In this paper, the initial-boundary value problem for a class of fourth-order nonlinear parabolic equations modeling the epitaxial growth of thin films is studied. By means of the theory of potential wells, the global existence, asymptotic behavior and finite time blow-up of weak solutions are obtained.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Reference32 articles.

1. L. Agélas.Global regularity of solutions of equation modeling epitaxy thin film growth in $\mathbb{R}^d$, $d = 1, 2$, J. Evol. Equ., 15 (2015), 89-106.

2. D. Blömker, C. Gugg.On the existence of solutions for amorphous molecular beam epitaxy, Nonlinear Anal. Real World Appl., 3 (2002), 61-73.

3. D. Blömker, C. Gugg, M. Raible.Thin-film-growth models: Roughness and correlation functions, Eur. J. Appl. Math., 13 (2002), 385-402.

4. M. Capiński, D. Gatarek.Stochastic equations in Hilbert space with applications to Navier-Stokes equation in any dimensions, J. Functional Anal., 126 (1994), 26-35.

5. H. Chen, H. Xu.Global existence and blow-up of solutions for infinitely degenerate semilinear pseudo-parabolic equations with logarithmic nonlinearity, Discrete Contin. Dyn. Syst., 39 (2019), 1185-1203.

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Asymptotic behaviors of global weak solutions for an epitaxial thin film growth equation;Nonlinear Analysis: Real World Applications;2025-02

2. Note on a nonlinear coupled 4th-order parabolic problem;Journal of Differential Equations;2024-06

3. A Class of Fractional Viscoelastic Kirchhoff Equations Involving Two Nonlinear Source Terms of Different Signs;Axioms;2024-03-05

4. Well-posedness and finite-time singularity of solutions in a 4th-order parabolic equation;Communications on Pure and Applied Analysis;2024

5. Note on a higher order pseudo‐parabolic equation with variable exponents;Mathematical Methods in the Applied Sciences;2023-06-15