Exponential Stability Results for a mixture of elastic solids with frictional dissipation
DOI:
https://doi.org/10.5540/03.2022.009.01.0261Keywords:
C0 Semigroup, Exponential stability, strong stability, mixture of solidsAbstract
We consider a mathematical model that describes a mixture of n elastic materials. We study the mixture problem with frictional damping. The problem consists of a linear system of n coupled hyperbolic partial differential equations. An existence and uniqueness result and an energy decay property are mentioned.
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References
F. F. Cordova Puma and Munoz Rivera J. E. “The lack of Polynomial Stability to mixtures with frictional dissipation”. In: J. Math. Anal. Appl. 446 (2017), pp. 1882–1897.
A. E. Green and P. M. Naghdi. “A note on mixtures”. In: International Journal of Eng. Sci. 6 (1998), pp. 631–635.
F. L. Huang. “Strong asymptotic stability theory for linear dynamical systems in Banach spaces”. In: Journal of Differential Equations vol. 104 (1993), pp. 307–324.
D. Iesan and R. Quintanilla. “Existence and continuous dependence results in the theory of interacting continua”. In: J. Elasticity 36(1) (1994), pp. 85–98.
Z. Liu and S. Zheng. Semigroups associated with dissipative system, Research Notes in Mathematics. vol. 398. Boca Raton, FL: Chapman and Hall/CRC, 1999.
A. Pazy. Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences. vol. 44. New York: Springer-Verlag, 1983.
J. Pruss. “On the spectrum of C0-Semigroups”. In: Trans. Amer. Math. Soc. 284 (1984), pp. 847–857.
R. Quintanilla. “Exponential decay in mixture with localized dissipative term”. In: Appl. Math. Lett. 8(12) (2005), pp. 1381–1388.
