Blow-up phenomena for a pseudo-parabolic equation with variable exponents. (February 2017)

• Record Type: Journal Article
• Authors: Di, Huafei; Shang, Yadong; Peng, Xiaoming
• Is Part Of: Applied mathematics letters. Volume 64(2017:Feb.)
• Page Start: 67
• Page End: 73
• Publication Date: 2017-02
• Subjects: Pseudo-parabolic equation -- Blow up -- Lower bound -- Variable exponent; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2016.08.013
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We consider a pseudo-parabolic equation with nonlinearities of variable exponent type u t − ν △ u t − div ( | ∇ u | m ( x ) − 2 ∇ u ) = | u | p ( x ) − 2 u, in Ω × ( 0, T ), associated with initial and Dirichlet boundary conditions. By means of a differential inequality technique, we obtain an upper bound for blow-up time if variable exponents p ( ⋅ ), m ( ⋅ ) and the initial data satisfy some conditions. Also, a lower bound for blow-up time is determined under some other conditions.