Abstract
This paper is concerned with a supercritical semilinear diffusion equation with the power nonlinearity. Via establishing a Liouville-type property, we prove the quasiconvergence (convergence to a set of steady states) of a large class of global solutions. The method of proof relies on similarity variables and invariant manifold ideas.
Original language | English (US) |
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Pages (from-to) | 194-214 |
Number of pages | 21 |
Journal | Journal of Differential Equations |
Volume | 208 |
Issue number | 1 SPEC.ISS. |
DOIs | |
State | Published - Jan 1 2005 |
Bibliographical note
Funding Information:This work was supported in part by the Japan Society of Promotion of Science.
Keywords
- Liouville property
- Quasiconvergence
- Semilinear heat equation
- Similarity variables