Advances in Differential Equations

On stabilization of solutions of the Cauchy problem for linear degenerate parabolic equations

S.D. Eidelman, S. Kamin, and A.F. Tedeev

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Abstract

We study the asymptotic behaviour of solutions to the Cauchy problem for linear degenerate parabolic equations. The coefficients of the equations may grow or tend to zero as $|x|\rightarrow \infty$. We establish necessary and sufficient conditions on the initial data which guarantee the stabilization of the solution to a constant.

Article information

Source
Adv. Differential Equations Volume 14, Number 7/8 (2009), 621-641.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867228

Mathematical Reviews number (MathSciNet)
MR2527687

Zentralblatt MATH identifier
1182.35035

Subjects
Primary: 35B40: Asymptotic behavior of solutions 35B45: A priori estimates 35K65: Degenerate parabolic equations 35K15: Initial value problems for second-order parabolic equations

Citation

Eidelman, S.D.; Kamin, S.; Tedeev, A.F. On stabilization of solutions of the Cauchy problem for linear degenerate parabolic equations. Adv. Differential Equations 14 (2009), no. 7/8, 621--641. https://projecteuclid.org/euclid.ade/1355867228.


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