Blow-Up of Solutions for a Class of Nonlinear Pseudoparabolic Equations with a Memory Term. (5th August 2014) - Di, Huafei; Shang, Yadong
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.