Asymptotic behaviour and exponential stability for a transmission problem in thermoelasticity

Marzocchi, Alfredo; Rivera, Jaime E. Mut̃oz; Naso, Maria Grazia

doi:10.1002/mma.323

Cited by 53 publications

(46 citation statements)

References 25 publications

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“…Asumiremos que f es una función de Lipschitz y µ > 0es una constante de Lipschitz y suficientemente pequeño. Análisis similares como en el referente [11] Marzacchi A, Muñoz R. Naso M. G., tenemos los Lema 5.1, Lema 5.2 y Lema 5.3.…”

Section: Estimativas De La Energíaunclassified

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Comportamiento asintótico y estabilidad exponencial para un problema de transmisión en termoelasticidad

et al. 2016

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Resumen: Estudiamos un problema termoelástica semi-lineal con amortiguación localizado, modelado porque es uno de los modelos matemáticos más importantes en la ciencia de los materiales.La existencia y decaimiento exponencial de la energía asociado al sistema se obtienen en el presente trabajo. Por otra parte, la existencia de conjuntos de absorción se logra en el caso no homogéneo.Palabras clave: Termoelasticidad, decaimiento exponencial, estabilidad asintótica. BEHAVIOR ASYMPTOTIC AND EXPONENTIAL STABILITY FOR A TRANSMISSION PROBLEM IN THERMOELASTICITYAbstract: We studied a semi-linear thermoelastic problem with localized damping, modelingwhich it is one of the most important in materials science mathematical models.The existence and exponential decay of the energy associated with the system are obtained in the present work. Moreover, the existence of sets of absorption is achieved in the non-homogeneous case.Keywords: Thermoelasticity; exponential decay; asymptotic behaviour. IntroducciónLa ecuación de onda sin ningún termino disipativo es un sistema conservativo, es decir, su energía total es constante para cualquier tiempo. Varios autores inducen diferentes tipos de mecanismos disipativos para estabilizar las oscilaciones. Por ejemplo, la disipación (o amortiguamiento) friccional αu t , actúa sobre todo el dominio ver Hansen [1], o las condiciones

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Section: Estimativas De La Energíaunclassified

“…El trabajo realizado por Marzocchi [11] es mejorado por un análisis más rigoroso en la obtención de la existencia y unicidad de solución del sistema planteado. Como por ejemplo la equivalencia de normas, estimativas de decaimiento y la existencia de solución débil y regularidad de soluciones y como también el espacio de soluciones.…”

Section: Conclusiónunclassified

Comportamiento asintótico y estabilidad exponencial para un problema de transmisión en termoelasticidad

et al. 2016

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“…Rivera and M.G. Naso [9], where authors showed stability results for a material consists of two components with thermoelastic properties, and one component at any temperature. In this sense, what we propose in this work is to study the wave propagation on a material consisting of three elastic components, which initially considered two of them with frictional dissipation.…”

Section: Introductionmentioning

confidence: 99%

Exponential decay of serially connected elastic wave

Fatori

Antonio²

2010

B Soc Paran Mat

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In this work we study a flexible structures which is formed by three serially connected elastic waves, more specifically on structure whose material consist of three different types of components where one is purely elastic component and two dissipative elastic. We show that for this types of materials the dissipation produced by the dissipative elastic part is strong enough to produce exponential decay of the solution, no matter how small is its size. We also show that the linear model is well posed.

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“…Similar to [21], according to the standard theory of ordinary differential equations, the finite dimensional…”

Section: Well-posedness Of the Problemmentioning

confidence: 99%

Well-posedness and general decay of solution for a transmission problem with viscoelastic term and delay

Wang¹,

Li²,

Zhu³

2016

J. Nonlinear Sci. Appl.

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In this paper, we consider a transmission problem in a bounded domain with a viscoelastic term and a delay term. Under appropriate hypotheses on the relaxation function and the relationship between the weight of the damping and the weight of the delay, we prove the well-posedness result by using FaedoGalerkin method. By introducing suitable Lyapunov functionals, we establish a general decay result, from which the exponential and polynomial types of decay are only special cases.

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Asymptotic behaviour and exponential stability for a transmission problem in thermoelasticity

Cited by 53 publications

References 25 publications

Comportamiento asintótico y estabilidad exponencial para un problema de transmisión en termoelasticidad

Comportamiento asintótico y estabilidad exponencial para un problema de transmisión en termoelasticidad

Exponential decay of serially connected elastic wave

Well-posedness and general decay of solution for a transmission problem with viscoelastic term and delay

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