Differential and Integral Equations
- Differential Integral Equations
- Volume 17, Number 5-6 (2004), 535-548.
Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation
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.
Differential Integral Equations, Volume 17, Number 5-6 (2004), 535-548.
First available in Project Euclid: 21 December 2012
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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