Blow-Up of Solutions for a Class of Nonlinear Pseudoparabolic Equations with a Memory Term

الملخص EN

We consider the nonlinear pseudoparabolic equation with a memory term ut-Δu-Δut+∫0tλt-τΔuτdτ=div∇up-2u+u1+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 function λ(t), we prove a finite-time blow-up result by using the concavity method.