Back to Search
Start Over
Properties of blow-up solutions and their initial data for quasilinear degenerate Keller–Segel systems of parabolic–parabolic type.
- Source :
-
Journal of Mathematical Analysis & Applications . Dec2018, Vol. 468 Issue 2, p585-607. 23p. - Publication Year :
- 2018
-
Abstract
- Abstract This paper is concerned with blow-up solutions to the quasilinear degenerate Keller–Segel systems of parabolic–parabolic type { u t = ∇ ⋅ (∇ u m − u q − 1 ∇ v) , x ∈ Ω , t > 0 , v t = Δ v − v + u , x ∈ Ω , t > 0 under homogeneous Neumann boundary conditions and initial conditions, where Ω ⊂ R N (N ≥ 3), m ≥ 1 , q ≥ 2. As the basis on this study, it was recently shown that there exist radial initial data such that the corresponding solutions blow up in the case q > m + 2 N ([5]). In the parabolic–elliptic case Sugiyama [27] established behavior of blow-up solutions; however, behavior in the parabolic–parabolic case has not been studied. The purpose of this paper is to give many finite-time blow-up solutions and behavior of blow-up solutions in a neighborhood of blow-up time in the parabolic–parabolic case. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 468
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 131730896
- Full Text :
- https://doi.org/10.1016/j.jmaa.2018.08.013