Global existence and nonexistence of solutions for the nonlinear pseudo‐parabolic equation with a memory term. (11th December 2014)

• Record Type: Journal Article
• Authors: Di, Huafei; Shang, Yadong
• Is Part Of: Mathematical methods in the applied sciences. Volume 38:Number 17(2015:Nov. 30)
• Page Start: 3923
• Page End: 3936
• Publication Date: 2014-12-11
• Subjects: existence and nonexistence -- pseudo‐parabolic -- memory term -- Galerkin method -- potential well theory; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3327
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we study the initial boundary value problem of nonlinear pseudo‐parabolic equation with a memory term u t − △ u − △ u t + ∫ 0 t λ ( t − τ ) △ u ( τ ) d τ = | u | p − 1 u, x ∈ Ω, t > 0 with initial conditions and Dirichlet boundary conditions. By the combination of the Galerkin method and Potential well theory, the existence of global solutions is derived. Moreover, not only the finite time blow up of solutions with the negative initial energy ( E (0) < 0) but also the finite time blow up results with the nonnegative initial energy (0≤ E (0) < d k ) are obtained by using Concavity method and Potential well theory. Copyright © 2014 John Wiley & Sons, Ltd.