Asymptotic behavior for a linear thermoelastic system
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Abstract
This article shows an extension of the results obtained from Bautista et al. (2022), for the linear thermoelastic system. It appears that the energy associated with the initial value problem is decreasing in time. Furthermore, it was shown that the solution déçues exponentially to zero in periodic Sobolev spaces: Hsp (0,2π)x Hsp (0,2π)x Hsp (0,2π), for all s ϵ R.
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References
Bautista, G., Fonseca, O., & Martínez, V. (2022) Buena colocación para un sistema termoelástico lineal con condiciones de frontera periódicas, Hatun Yachay Wasi, 1(2), 94–108. https://doi.org/10.57107/hyw.v1i2.27.
Cazenave, T. & Haraux, A. (1998). An introduction to semilinear evolution equations, Oxford Lecture Series in Mathematics and its Applications, 13, The Clarendon Press, Oxford University Press, New York.
Micu, S. & Pazoto, A. (2017). Stabilization of a Boussinesq system with generalized damping, Systems Control Letters, 105, 62-69. https://doi.org/10.1016/j.sysconle.2017.04.012.
Muñoz, J. (1992). Energy decay rates in linear thermoelasticity, Funkcial Ekvac, 35, 19-30. http://www.im.ufrj.br/~rivera/Art_Pub/funkcTer.pdf.
Pazy, A. (1983). Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, 44, SpringerVerlag: New York-Berlin-Heidelberg-Tokyo. http://dx.doi.org/10.1007/978-1-4612-5561-1.
Racke, R. & Shibata, Y. (1991). Global smooth solutions and asymptotic stability in onedimensional nonlinear thermoelasticity. Archive for Rational Mechanics and Analysis, 116, 1-34. https://doi.org/10.1007/BF00375601.