Galerkin method for nonlocal mixed boundary value problem for the Moore‐Gibson‐Thompson equation with integral condition

Abstract

In this paper, we are going to deal with the nonlocal mixed boundary value problem for the Moore‐Gibson‐Thompson equation. Galerkin method was the main used tool for proving the solvability of the given nonlocal problem.

Elastic membrane equation with dynamic boundary conditions and infinite memory

“…The same arguments as in [5], [15] and [32], we can prove the global existence of solutions to problem (1.5) − (1.8) given in the following theorem.…”

General Decay of the Moore–Gibson–Thompson Equation with Viscoelastic Memory of Type II

“…Natural questions can be asked based on the study of the viscoelastic memory and integral condition system (see [7][8][9][10]): could the addition of the memory kernel of type II harm the stability of this kind of problem in any way? If the answer to the question in the wave condition with friction damping are relatively simple, it is not easy to answer in the case of memory kernel of type II that we present below, especially in Fourier space.…”

The Galerkin Method for Fourth-Order Equation of the Moore–Gibson–Thompson Type with Integral Condition

“…These problems can be encountered in many scientific domains and many engineering models (see previous works [5, 25-32, 35, 36, 40, 41]). Mesloub and Mesloub in [33] have applied the Galerkin method to a higher dimension mixed with nonlocal problem for a Boussinesq equation, while Boulaaras et al investigated the Moore-Gibson-Thompson equation with the integral condition in [4]. Motivated by these outcomes, we improve the existence and uniqueness by the Galerkin method of the fourth-order equation of the Moore-Gibson-Thompson type with integral condition; this problem was cited by the work of Dell'Oro and Pata in [9].…”