Global existence, blow-up and optimal decay for a nonlinear viscoelastic equation with nonlinear damping and source term

Global existence, decay and blow up solutions for coupled nonlinear wave equations with damping and source terms

We study the initial-boundary value problem for a system of nonlinear wave equations with nonlinear damping and source terms, in a bounded domain. The decay estimates of the energy function are established by using Nakao’s inequality. The nonexistence of global solutions is discussed under some conditions on the given parameters.

Blow up and global existence in a nonlinear viscoelastic wave equation

where a, b > 0, p > 2, m ≥ 1, and Ω is a bounded domain of R (n ≥ 1), with a smooth boundary ∂Ω. In the absence of the viscoelastic term (g = 0), the problem has been extensively studied and results concerning existence and nonexistence have been established. For a = 0, the source term bu |u|p−2 causes finite time blow up of solutions with negative initial energy (see [2], [8]). For b = 0, the ...

Blow-up of Solutions to a Coupled Quasilinear Viscoelastic Wave System with Nonlinear Damping and Source

We study the blow-up of the solution to a quasilinear viscoelastic wave system coupled by nonlinear sources. The system is of homogeneous Dirichlet boundary condition. The nonlinear damping and source are added to the equations. We assume that the relaxation functions are non-negative non-increasing functions and the initial energy is negative. The competition relations among the nonlinear prin...

Global Solutions and Blow-up Profiles for a Nonlinear Degenerate Parabolic Equation with Nonlocal Source

This paper deals with a degenerate parabolic equation vt = ∆v + av1 ∥v∥1 α1 subject to homogeneous Dirichlet condition. The local existence of a nonnegative weak solution is given. The blow-up and global existence conditions of nonnegative solutions are obtained. Moreover, we establish the precise blow-up rate estimates for all the blow-up solutions.

Existence and Uniform Decay of Solutions of a Parabolic-Hyperbolic Equation with Nonlinear Boundary Damping and Boundary Source Term