Differential and Integral Equations

Non-accessible singular homoclinic orbits for a semilinear parabolic equation

Marek Fila and Eiji Yanagida

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Abstract

We show the existence of at least three different continuations beyond blow-up for a backward self-similar solution of a supercritical Fujita equation. One of these extended solutions cannot be approximated by classical entire solutions in a specific way given by the scaling invariance of the equation, while the minimal continuation is known to be accessible by a family of such entire solutions.

Article information

Source
Differential Integral Equations, Volume 27, Number 5/6 (2014), 563-578.

Dates
First available in Project Euclid: 3 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.die/1396558097

Mathematical Reviews number (MathSciNet)
MR3189532

Zentralblatt MATH identifier
1340.35179

Subjects
Primary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35B44: Blow-up 35K55: Nonlinear parabolic equations 37C29: Homoclinic and heteroclinic orbits

Citation

Fila, Marek; Yanagida, Eiji. Non-accessible singular homoclinic orbits for a semilinear parabolic equation. Differential Integral Equations 27 (2014), no. 5/6, 563--578. https://projecteuclid.org/euclid.die/1396558097


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