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

Abstract

This paper studies the system of coupled nondegenerate viscoelastic Kirchhoff equations with a distributed delay. By using the energy method and Faedo-Galerkin method, we prove the global existence of solutions. Furthermore, we prove the exponential stability result.

Controllability of Stochastic Delay Systems Driven by the Rosenblatt Process

“…Due to its effective modeling in numerous fields of science and engineering, including economics, biology, physics, medicine, finance, fluid dynamics, etc., stochastic delaydifferential equations and their applications have received a great deal of attention; see, for instance, [1][2][3][4][5][6][7][8][9][10]. The concept of the controllability of systems is one of the most fundamental and important concepts in contemporary control theory, which involves figuring out the control parameters that directly a control system's solutions from their initial state to their final state using the set of permissible controls, where initial and final states may vary across the entire space.…”

Well-Posedness and Stability Result of the Nonlinear Thermodiffusion Full von Kármán Beam with Thermal Effect and Time-Varying Delay

“…And it is more convenient to work in the history space setting by introducing the so-called summed past history of θ and P defined by (see [31][32][33][34][35][36])…”

“…Condition ( 28) is needed to stabilize the system when diffusion effects are added to thermal effects (see, e.g., [31][32][33][34][35][36][37][38] for more information on this). By virtue of cr > d 2 , we deduce that d/c < r/d.…”

Exponential Stabilization of a Swelling Porous-Elastic System with Microtemperature Effect and Distributed Delay

“…Also, there are many works that have studied this type of problems, of which [11,[15][16][17][18][19][20][21][22][23][24].…”