Global existence blow up and extinction for a class of thin-film equation. (December 2016)

• Record Type: Journal Article
• Authors: Li, Qingwei; Gao, Wenjie; Han, Yuzhu
• Is Part Of: Nonlinear analysis. Volume 147(2016)
• Page Start: 96
• Page End: 109
• Publication Date: 2016-12
• Subjects: primary 35J15 -- secondary 35J20 35J70; Thin-film equation -- Potential wells -- Global existence -- Uniqueness -- Blow up; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.08.021
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we use the modified method of potential wells to study the properties of solutions for a class of higher order nonlinear parabolic equations with p -Laplace term − ( | u x | p − 2 u x ) x and nonlocal source | u | q − 1 u − 1 ∣ Ω ∣ ∫ Ω | u | q − 1 u d x . Global existence, uniqueness, blow up in finite time and asymptotic behavior of solutions will be proved under different initial conditions. Furthermore, a numerical example is given to illustrate the blow-up of solutions in finite time.