Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Parabolic evolution equations with asymptotically autonomous delay


Author: Roland Schnaubelt
Journal: Trans. Amer. Math. Soc. 356 (2004), 3517-3543
MSC (2000): Primary 35R10; Secondary 34K30, 47D06
Published electronically: November 25, 2003
MathSciNet review: 2055745
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Abstract: We study retarded parabolic non-autonomous evolution equations whose coefficients converge as $t\to\infty$, such that the autonomous problem in the limit has an exponential dichotomy. Then the non-autonomous problem inherits the exponential dichotomy, and the solution of the inhomogeneous equation tends to the stationary solution at infinity. We use a generalized characteristic equation to deduce the exponential dichotomy and new representation formulas for the solution of the inhomogeneous equation.


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Additional Information

Roland Schnaubelt
Affiliation: FB Mathematik und Informatik, Martin-Luther-Universität, 06099 Halle, Germany
Email: schnaubelt@mathematik.uni-halle.de

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03512-8
Keywords: Retarded parabolic evolution equation, asymptotically autonomous, exponential dichotomy, robustness, convergence of solutions, variation of parameters formula, characteristic equation, evolution semigroup
Received by editor(s): January 18, 2002
Received by editor(s) in revised form: March 27, 2003
Published electronically: November 25, 2003
Article copyright: © Copyright 2003 American Mathematical Society