Multiscale Asymptotic Behavior of a Solution of the Heat Equation on $$ \mathbb{R}^N $$
Thierry Cazenave, Flávio Dickstein, Fred B. Weissler · Progress in nonlinear differential equations and their applications · 2005
In this paper, we construct solutions e t∆ u of the heat equation on $$ \mathbb{R}^N $$ , where $$ u \in C_0 \left( {\mathbb{R}^N } \right) $$ , which have nontrivial asymptotic properties on different time scales. More precisely, for all 0<σ