Differential and Integral Equations

Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation

P. Poláčik and E. Yanagida

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Abstract

This paper is concerned with a supercritical semilinear diffusion equation. We show the existence of a solution that undergoes a birth-and-death process of a single peak emerging at arbitrarily prescribed positions and heights. In particular the solution has no asymptotic center of radial symmetry as time approaches infinity. We also construct a solution with arbitrarily prescribed grow-up set.

Article information

Source
Differential Integral Equations Volume 17, Number 5-6 (2004), 535-548.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060346

Mathematical Reviews number (MathSciNet)
MR2054933

Zentralblatt MATH identifier
1174.35403

Subjects
Primary: 35K57: Reaction-diffusion equations
Secondary: 35B33: Critical exponents 35K15: Initial value problems for second-order parabolic equations

Citation

Poláčik, P.; Yanagida, E. Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation. Differential Integral Equations 17 (2004), no. 5-6, 535--548. https://projecteuclid.org/euclid.die/1356060346.


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