In this paper we give the precise description of the large time behavior of the solution u of the Cauchy problem by using the ordinary differential equation ζ '=-ζ β and a linear parabolic equation. Here N≥1, a∈R N, α>1, β>1, λ>0, and φ is a bounded continuous function such that φ∈L p(R N) for some 1≤p<∞. Furthermore, we study the large time behavior of the hot spots for the solution u.
ASJC Scopus subject areas
- Applied Mathematics