Local existence and blow up of solutions for a coupled viscoelastic Kirchhoff-type equation with degenerate damping

Abstract

In this paper, we consider the initial boundary value problem of a coupled viscoelastic Kirchhoff-type equations with degenerate damping:. Firstly, we prove a local existence theorem by using the Faedo-Galerkin approximations. Then, we study blow up of solutions when initial energy is positive.

Global Existence And Growth Of Solutions To Coupled Degeneratly Damped Klein-Gordon Equations

“…From ( 7) and ( 8), we have Then, since (9) we have 𝐼(𝑡 ) > 0 which contradicts to (13). So, 𝐼(𝑡) > 0 𝑜𝑛 [0, 𝑇].…”

Blow up and Exponential Growth to a Kirchhoff-Type Viscoelastic Equation with Degenerate Damping Term

“…The authors discussed global existence, general decay and blow up results of solutions. Recently, Piskin and Ekinci [19] considered same problem and proved local existence result. In [20], the author studied blow up of solutions with positive initial energy for problem (1.5) without viscoelastic term.…”

“…Recently, Piskin and Ekinci [19] considered same problem and proved local existence result. In [20], the author studied blow up of solutions with positive initial energy for problem (1.5) without viscoelastic term. In addition, they gave some estimates for lower bound of the blow up time.…”

Coupled system of nonlinear viscoelastic plate equations of (p(x),q(x))‐Kirchhoff‐type: Global existence, general decay, and blow‐up

“…They obtained their results without imposing any growth condition on the weak damping term at the origin. See also earlier studies [25–30] and references therein.…”