Existence, Nonexistence, and Stability of Solutions for a Delayed Plate Equation with the Logarithmic Source

Abstract

In this work, we study a plate equation with time delay in the velocity, frictional damping, and logarithmic source term. Firstly, we obtain the local and global existence of solutions by the logarithmic Sobolev inequality and the Faedo-Galerkin method. Moreover, we prove the stability and nonexistence results by the perturbed energy and potential well methods.

Local existence, global existence and decay results of a logarithmic wave equation with delay term

“…Moreover, in Messaoudi et al, 18 they extended the results obtained to the case of distributed delay $$$ \left({\int}_{\tau_1}^{\tau_2}{\mu}_2(s)\Delta {u}_t\left(x,t-s\right) ds\right) $$$. Recently, some other researchers studied delayed hyperbolic‐type equations (see previous works 19–25 ).…”

“…Recently, some other researchers studied delayed hyperbolic-type equations (see previous works [19][20][21][22][23][24][25] ). Motivated by previous works and in the presence of strong damping (−𝜇 1 Δu t (x, t)), delay (−𝜇 2 Δu t (x, t − 𝜏)), and logarithmic source (u|u| p−2 ln |u| k ) terms, we prove the local existence, global existence, and exponential decay for the wave equation (1).…”

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.…”

Existence and asymptotic behaviour of solutions for the wave equation with a time varying delay and logarithmic nonlinearity

“…Recently, Yüksekkaya [15] improved the earlier result of [14] by considering the term ∆ 2 u in (1.5) as follows:…”