Blow-Up of Solutions for a Class of Nonlinear Pseudoparabolic Equations with a Memory Term. (5th August 2014)

• Record Type: Journal Article
• Authors: Di, Huafei; Shang, Yadong
• Other Names: Dong BoQing Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-08-05
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/507494
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We consider the nonlinear pseudoparabolic equation with a memory termu t - Δ u - Δ u t + ∫ 0 t λ t - τ Δ u τ d τ = d i v ∇ u p - 2 u + u 1 + α, x ∈ Ω, t > 0, with an initial condition and Dirichlet boundary condition. Under negative initial energy and suitable conditions on p, α, and the relaxation functionλ ( t ), we prove a finite-time blow-up result by using the concavity method.