Advances in Differential Equations

Exponential decay for a von Kármán system with memory

Jaime E. Muñoz Rivera and Yolanda S. Santiago Ayala

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Abstract

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.

Article information

Source
Adv. Differential Equations Volume 9, Number 9-10 (2004), 1115-1142.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867915

Mathematical Reviews number (MathSciNet)
MR2098067

Zentralblatt MATH identifier
1103.35096

Subjects
Primary: 35Q72
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

Citation

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.


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