Asymptotic Behavior and Blow-Up of Solutions for a Nonlinear Viscoelastic Wave Equation With Boundary Dissipation

Tahamtani, Faramarz

doi:10.11650/tjm.17.2013.3034

Cited by 26 publications

(8 citation statements)

References 20 publications

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“…For wave equations with various dissipations, many results concerning stabilization of solutions have been proved. Recently, wave equations with viscoelastic damping have been investigated by many authors, see [2,4,3,9,8,10,16,18] and the references therein. It is showed that the dissipation produced by the viscoelastic part can produce the decay of the solution.…”

Section: Exponential Stabilitymentioning

confidence: 99%

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Exponential Stability of a Transmission Problem with History and Delay

Bahri

Beniani

2019

Stat., optim. inf. comput.

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Section: Exponential Stabilitymentioning

confidence: 99%

“…We just need to prove that (21) has a solution (u, v) ∈ X * and replace in (18), (19) and 20to (16). Consequently, problem (21) is equivalent to the problem…”

mentioning

confidence: 99%

Exponential Stability of a Transmission Problem with History and Delay

Bahri

Beniani

2019

Stat., optim. inf. comput.

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“…the authors obtained that the semigroup decays as 1 √ t . We refer the reader to [1,5,6,8,10,11,14,16,17,19,24,26] for some other related results. Motivated by the above results, we intend to study the well-posedness and the asymptotic stability of the thermoelastic laminated beam system either with or without structural damping, where the heat flux is given by Fourier's law.…”

Section: Introductionmentioning

confidence: 99%

Exponential and Polynomial Decay for a Laminated Beam with Fourier's Type Heat Conduction

Liu¹,

Zhao²

2019

Preprint

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In this paper, we study the well-posedness and asymptotics of a one-dimensional thermoelastic laminated beam system either with or without structural damping, where the heat conduction is given by Fourier's law effective in the rotation angle displacements. We show that the system is well-posed by using Lumer-Philips theorem, and prove that the system is exponentially stable if and only if the wave speeds are equal, by using the perturbed energy method and Gearhart-Herbst-Prüss-Huang theorem. Furthermore, we show that the system with structural damping is polynomially stable provided that the wave speeds are not equal, by using the second-order energy method.

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“…Segundo probamos la propiedad de explosión de soluciones en tiempo …nito, mediante el método directo de la energía, desarrollado por Li y Tsai [6], bajo algunas restricciones a los datos iniciales y para la energía inicial relativamente arbitraria. En la discusión del problema (1.1) (1.4), empleamos las estrategias y técnicas inspiradas en los trabajos de Park and Park [7], Wu [11] y Tahamtani y Peyravi [10].…”

Section: Introductionunclassified

No Existencia Global para una Ecuación de Onda Viscoelástica con Frontera Disipativa

Méndez

2016

Pesquimat

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Resumen: Consideramos un problema mixto para una ecuación de onda no lineal viscoelástica con condiciones de frontera disipativa lineal y término fuente no lineal. Probamos la existencia y unicidad de su solución local por el método de Faedo-Galerkin y mostramos la explosión de soluciones por el método de la energía.Palabras clave: Ecuación de onda viscoelástica, solución local, método de Faedo-Galerkin, explosión de soluciones, método de la energía. Global Nonexistence for a Viscoelastic Wave Equation with Boundary DissipativeAbstract: We consider a mixed problem for a viscoelastic nonilinear wave equation with boundary dissipative lineal and nonlinear source term. We prove the existence and uniqueness of its local solution by the Faedo-Galerkin method and show the blow-up of solutions by the energy method.Keywords: Viscoelastic wave equation, local solution, Faedo-Galerkin method, blow-up of solutions, energy method. IntroducciónEn este artículo, consideramos el problema para la siguiente ecuación de onda viscoelástica:donde es un conjunto abierto y acotado de R n con frontera regular @ = 0 [ 1 , 0 y 1 son cerrados, disjuntos y con medidas positivas, es el operador Laplaciano, r es el operador gradiente, div es el operador divergencia, g (t) es una función real continua no negativa para

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Asymptotic Behavior and Blow-Up of Solutions for a Nonlinear Viscoelastic Wave Equation With Boundary Dissipation

Cited by 26 publications

References 20 publications

Exponential Stability of a Transmission Problem with History and Delay

Exponential Stability of a Transmission Problem with History and Delay

Exponential and Polynomial Decay for a Laminated Beam with Fourier's Type Heat Conduction

No Existencia Global para una Ecuación de Onda Viscoelástica con Frontera Disipativa

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Asymptotic Behavior and Blow-Up of Solutions for a Nonlinear Viscoelastic Wave Equation With Boundary Dissipation

Cited by 26 publications

References 20 publications

Exponential Stability of a Transmission Problem with History and Delay

Exponential Stability of a Transmission Problem with History and Delay

Exponential and Polynomial Decay for a Laminated Beam&nbsp;with Fourier's Type Heat Conduction

No Existencia Global para una Ecuación de Onda Viscoelástica con Frontera Disipativa

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Exponential and Polynomial Decay for a Laminated Beam with Fourier's Type Heat Conduction