Taiwanese Journal of Mathematics

EXPONENTIAL STABILITY OF SOLUTIONS TO SEMILINEAR PARABOLIC EQUATIONS WITH DELAYS

Cung The Anh and Le Van Hien

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Abstract

In this paper we prove the global existence and the global exponential stability of weak solutions to a class of semilinear parabolic equations with discrete and distributed time-varying delays. Moreover, the exponential stability of stationary solutions of the equations is also studied. The obtained results can be applied to some models in biology and physics.

Article information

Source
Taiwanese J. Math., Volume 16, Number 6 (2012), 2133-2151.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406844

Digital Object Identifier
doi:10.11650/twjm/1500406844

Mathematical Reviews number (MathSciNet)
MR3001840

Zentralblatt MATH identifier
1261.35022

Subjects
Primary: 35B35: Stability 37L15: Stability problems

Keywords
PDEs with delays weak solution stationary solution exponential stability Galerkin method Lyapunov-Krasovskii functional

Citation

Anh, Cung The; Hien, Le Van. EXPONENTIAL STABILITY OF SOLUTIONS TO SEMILINEAR PARABOLIC EQUATIONS WITH DELAYS. Taiwanese J. Math. 16 (2012), no. 6, 2133--2151. doi:10.11650/twjm/1500406844. https://projecteuclid.org/euclid.twjm/1500406844


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