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.
Bibliographical noteFunding Information:
This work was supported in part by the Japan Society of Promotion of Science.
- Liouville property
- Semilinear heat equation
- Similarity variables