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Exponential decay of a solution for some parabolic equation involving a time nonlocal term

Kota Kumazaki (2015)

Mathematica Bohemica

We consider the large time behavior of a solution of a parabolic type equation involving a nonlocal term depending on the unknown function. This equation is proposed as a mathematical model of carbon dioxide transport in concrete carbonation process, and we proved the existence, uniqueness and large time behavior of a solution of this model. In this paper, we derive the exponential decay estimate of the solution of this model under restricted boundary data and initial data.

Exponential decay of energy for some nonlinear hyperbolic equations with strong dissipation.

Ye, Yaojun (2010)

Advances in Difference Equations [electronic only]

Exponential decay of solutions to a fourth-order viscoelastic evolution equation in $ℝ^{n}$ .

Kafini, Mohammad (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Exponential decay to partially thermoelastic materials

Jaime E. Muñoz Rivera, Vanilde Bisognin, Eleni Bisognin (2002)

Bollettino dell'Unione Matematica Italiana

We study the thermoelastic system for material which are partially thermoelastic. That is, a material divided into two parts, one of them a good conductor of heat, so there exists a thermoelastic phenomenon. The other is a bad conductor of heat so there is not heat flux. We prove for such models that the solution decays exponentially as time goes to infinity. We also consider a nonlinear case.

Exponential stability for the wave equation with weak nonmonotone damping.

Martinez, P., Vancostenoble, J. (2000)

Portugaliae Mathematica

Exponential stability of a flexible structure with history and thermal effect

Roberto Díaz, Jaime Muñoz, Carlos Martínez, Octavio Vera (2020)

Applications of Mathematics

In this paper we study the asymptotic behavior of a system composed of an integro-partial differential equation that models the longitudinal oscillation of a beam with a memory effect to which a thermal effect has been given by the Green-Naghdi model type III, being physically more accurate than the Fourier and Cattaneo models. To achieve this goal, we will use arguments from spectral theory, considering a suitable hypothesis of smoothness on the integro-partial differential equation.