Advances in Differential Equations

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

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

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.