Limit behavior of the solution to nonlinear viscoelastic Marguerre–von Kármán shallow shell system

Abstract

This paper is concerned with the nonlinear full Marguerre-von Kármán shallow shell system with a dissipative mechanism of memory type. The model depends on one small parameter. The main purpose of this paper is to show that as the parameter approaches zero, the limiting system is the well-known full von Kármán model with memory for thin plates.

Global existence uniqueness and decay estimates for nonlinear viscoelastic wave equation with boundary dissipation

“…In [25][26][27], we considered a model of nonlinear viscoelastic shallow shell that is referred to as the full Marguerre-von Kármán under the presence of long-time memory. We proved global existence and uniqueness of its weak solution and showed that the energy functional associated with the system decays exponentially to zero as time goes to infinity, we also proved that as the parameter approaches zero, the limiting system is the well-known full von Marguerre-von Kármán model with memory for thin plates.…”

Uniform energy decay rates for nonlinear viscoelastic wave equation with nonlocal boundary damping

“…In [20,21], we considered a model of nonlinear viscoelastic shallow shell that is referred to as the full Marguerre-von Kármán under the presence of long-time memory. We showed that the energy functional associated with the system decays exponentially to zero as time goes to infinity and proved that as the parameter approaches zero, the limiting system is the well-known full von Kármán model with memory for thin plates.…”

Exact Solutions of the Vakhnenko-Parkes Equation with Complex Method

“…It has aroused extensive interest in the study of nonlinear differential equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”