General decay of solution for a transmission problem in infinite memory-type thermoelasticity with second sound

In the present paper, we consider an important problem from the point of view of application in sciences and engineering, namely, a new class of nonlinear Love-equation with infinite memory in the presence of source term that takes general nonlinearity form. New minimal conditions on the relaxation function and the relationship between the weights of source term are used to show a very general decay rate for solution by certain properties of convex functions combined with some estimates. Investigations on the propagation of surface waves of Love-type have been made by many authors in different models and many attempts to solve Love’s equation have been performed, in view of its wide applicability. To our knowledge, there are no decay results for damped equations of Love waves or Love type waves. However, the existence of solution or blow up results, with different boundary conditions, have been extensively studied by many authors. Our interest in this paper arose in the first place in consequence of a query for a new decay rate, which is related to those for infinite memory ϖ in the third section. We found that the system energy decreased according to a very general rate that includes all previous results.

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A general decay estimate for the nonlinear transmission problem of weak viscoelastic equations with time-varying delay

Journal of Mathematical Physics ◽

10.1063/1.5103177 ◽

2019 ◽

Vol 60 (10) ◽

pp. 101507 ◽

Cited By ~ 1

Author(s):

Zhiqing Liu ◽

Cunchen Gao ◽

Zhong Bo Fang

Keyword(s):

Decay Estimate ◽

General Decay ◽

Transmission Problem ◽

Time Varying ◽

Nonlinear Transmission ◽

Time Varying Delay ◽

Viscoelastic Equations ◽

Varying Delay

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General decay for Kirchhoff plates with a boundary condition of memory type

Boundary Value Problems ◽

10.1186/1687-2770-2012-129 ◽

2012 ◽

Vol 2012 (1) ◽

Cited By ~ 9

Author(s):

Jum-Ran Kang

Keyword(s):

Boundary Condition ◽

General Decay ◽

Kirchhoff Plates ◽

Memory Type

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General decay in a Timoshenko-type system with thermoelasticity with second sound

Advances in Nonlinear Analysis ◽

10.1515/anona-2015-0038 ◽

2015 ◽

Vol 4 (4) ◽

pp. 263-284 ◽

Cited By ~ 6

Author(s):

Mohamed Ali Ayadi ◽

Ahmed Bchatnia ◽

Makram Hamouda ◽

Salim Messaoudi

Keyword(s):

Group Theory ◽

Type System ◽

General Decay ◽

Regularity Of Solutions ◽

Well Posedness ◽

Second Sound ◽

Semi Group ◽

Stability Number ◽

Timoshenko System ◽

Relaxation Functions

AbstractIn this article, we consider a vibrating nonlinear Timoshenko system with thermoelasticity with second sound. We discuss the well-posedness and the regularity of solutions using the semi-group theory. Moreover, we establish an explicit and general decay result for a wide class of relaxation functions, which depend on a stability number μ.

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