Advances in Differential Equations

Isolated boundary singularities of signed solutions of some semilinear parabolic equations

Moshe Marcus and Laurent Véron

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Abstract

We investigate the singular behaviour of any solution of the semilinear parabolic equation $u_{t}-\Delta u+\left| u\right| ^{q-1}u=0$ in a cylindrical domain near a boundary point. The description is made by means of explicit self-similar solutions of the same equation into a half-space. Uniqueness of singular solutions is also proven.

Article information

Source
Adv. Differential Equations Volume 6, Number 11 (2001), 1281-1316.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1357139962

Mathematical Reviews number (MathSciNet)
MR1859349

Zentralblatt MATH identifier
1009.35044

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35K20: Initial-boundary value problems for second-order parabolic equations 35K60: Nonlinear initial value problems for linear parabolic equations

Citation

Marcus, Moshe; Véron, Laurent. Isolated boundary singularities of signed solutions of some semilinear parabolic equations. Adv. Differential Equations 6 (2001), no. 11, 1281--1316. https://projecteuclid.org/euclid.ade/1357139962.


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