Existence, Decay, and Blow-Up of Solutions for a Higher-Order Kirchhoff-Type Equation with Delay Term

Abstract

This article deals with the study of the higher-order Kirchhoff-type equation with delay term in a bounded domain with initial boundary conditions, where firstly, we prove the global existence result of the solution. Then, we discuss the decay of solutions by using Nakao’s technique and denote polynomially and exponentially. Furthermore, the blow-up result is established for negative initial energy under appropriate conditions.

Existence and exponential decay of a logarithmic wave equation with distributed delay

“…Furthermore, in [21], they extended the results obtained to the case of strong delay (µ 2 ∆u t (x,t − τ)) in same work. Some other researchers considered delayed hyperbolic-type equations (see [2,14,15,25,27,[29][30][31][32][33][34]).…”

Stability Result for a Kirchhoff Beam Equation with Variable Exponent and Time Delay

“…in a non-cylindrical domain. Recently, some other authors investigate hyperbolic type equations (see [11,[21][22][23][24][25]28]). Our aim in this work is to prove the stability of solutions for the Kirchhoff beam equation with the delay term (µ 2 u t (x,t − τ)) and variable exponents which make the problem more different than from those considered in the literature.…”