Advances in Differential Equations
- Adv. Differential Equations
- Volume 9, Number 9-10 (2004), 1115-1142.
Exponential decay for a von Kármán system with memory
In this paper we consider the Von Kármán system with thermal effect. The constitutive assumptions we use for the propagation of temperature were proposed by Gurtin and Pipkin. In this case the heat conduction is independent of the present values of the temperature gradient. We show that the corresponding nonlinear system is globally well posed. Moreover, when the relaxation function which characterizes the memory effect on the temperature decays exponentially, then we show that the solution of the system also decays exponentially.
Adv. Differential Equations Volume 9, Number 9-10 (2004), 1115-1142.
First available in Project Euclid: 18 December 2012
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Secondary: 35B40: Asymptotic behavior of solutions 35D05 35G25: Initial value problems for nonlinear higher-order equations 74D05: Linear constitutive equations 74F05: Thermal effects 74H40: Long-time behavior of solutions
Santiago Ayala, Yolanda S.; Muñoz Rivera, Jaime E. Exponential decay for a von Kármán system with memory. Adv. Differential Equations 9 (2004), no. 9-10, 1115--1142. https://projecteuclid.org/euclid.ade/1355867915.