We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Global Existence and Asymptotic Behavior of Solutions to the Hyperbolic Keller-Segel Equation with a Logistic Source.
- Authors
Chae, Myeongju
- Abstract
In this paper we consider a hyperbolic Keller-Segel system with a logistic source in two dimension. We show the system has a global smooth solution upon small perturbation around a constant equilibrium and the solution satisfies a dissipative energy inequality. To do this we find a convex entropy functional and a compensating matrix, which transforms the partially dissipative system into a uniformly dissipative one. Those two ingredients were crucial for the study of a partially dissipative hyperbolic system (Hanouzet and Natalini in Arch. Ration. Mech. Anal. 169(2):89-117, 2003; Kawashima in Ph.D. Thesis, Kyoto University, 1983; Yong in Arch. Ration. Mech. Anal. 172(2):247-266, 2004).
- Subjects
HYPERBOLIC differential equations; EQUILIBRIUM; PERTURBATION theory; ENERGY dissipation; NUMERICAL solutions to hyperbolic differential equations; ENTROPY power inequality; ENTROPY
- Publication
Acta Applicandae Mathematicae, 2018, Vol 158, Issue 1, p207
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-018-0180-3