Differential and Integral Equations

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

P. Poláčik and E. Yanagida

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

Export citation