Global well‐posedness and exponential stability results of a class of Bresse‐Timoshenko‐type systems with distributed delay term

Abstract

In this paper, we consider a Bresse‐Timoshenko‐type system with distributed delay term. Under suitable assumptions, we establish the global well‐posedness of the initial and boundary value problem by using the Faedo‐Galerkin approximations and some energy estimates. By using the energy method, we show two exponential stability results for the system with delay in vertical displacement and in angular rotation, respectively. This extends earlier results in the literature.

Well-Posedness and Stability Results for Lord Shulman Swelling Porous Thermo-Elastic Soils with Microtemperature and Distributed Delay

“…Time delays are of significant importance in the majority of natural phenomena and industrial systems, as they have the potential to induce instability and should be treated with utmost consideration. Additionally, there are numerous works that have examined this category of issues, including [17][18][19][20][21][22][23].…”

Well posedness and stability result for a microtemperature full von Kármán beam with infinite‐memory and distributed delay terms

“…For more depth, you can refer to the previous papers. 3,4,10,15,[20][21][22][23][24][25][26] Recently, in the presence of the both memory and the distributed delay and in absence of the microtemperature, Lekdim and Khemmoudj 7 proved the existence and the uniquneness by Faedo-Galerkin method of our problem (1.1) and established the exponential stability of the solutions.…”

“…They prove many results for the existence and asymptotic behavior of solutions (exponential or polynomial) under appropriate assumptions for the delay function. For more depth, you can refer to the previous papers 3,4,10,15,20–26 …”

On the System of Coupled Nondegenerate Kirchhoff Equations with Distributed Delay: Global Existence and Exponential Decay

“…Also, the time or delay recorded in many natural and physical phenomena, especially problems resulting from vibrations, is an important factor for stability in general. And it has been studied extensively by many authors, including [5][6][7][11][12][13][14][15][16][17][18][19][20][21]. Recently, in the presence of the varying delay, Mezouar and Boularrass studied system (1); for more information, see [22].…”