Nonparabolic Asymptotic Limits of Solutions of the Heat Equation on $${mathbb{R}}^N$$期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Nonparabolic Asymptotic Limits of Solutions of the Heat Equation on $${mathbb{R}}^N$$

Authors:	Thierry Cazenave Flávio Dickstein Fred B. Weissler

Affiliation:	(1) Laboratoire Jacques-Louis Lions, UMR CNRS 7598, B.C. 187, Université Pierre et Marie Curie, 4, place Jussieu, 75252 Paris Cedex 05, France;(2) Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21944-970 Rio de Janeiro, RJ, Brazil;(3) LAGA UMR CNRS 7539, Institut Galilée–Université Paris XIII, 99, Avenue J.-B. Clément, 93430 Villetaneuse, France

Abstract:	In this paper, we construct solutions u(t,x) of the heat equation on ${mathbb{R}}^N$ such that $t^{frac {mu } {2}} u(t, xt^beta )$ has nontrivial limit points in $C_0({mathbb{R}}^N)$ as t → ∞ for certain values of μ > 0 and β > 1/2. We also show the existence of solutions of this type for nonlinear heat equations.

Keywords:	Heat equation asymptotic behavior rescaling
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