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NO CRITICAL NONLINEAR DIFFUSION IN 1D QUASILINEAR FULLY PARABOLIC CHEMOTAXIS SYSTEM.
- Source :
-
Proceedings of the American Mathematical Society . Jun2018, Vol. 146 Issue 6, p2529-2540. 12p. - Publication Year :
- 2018
-
Abstract
- This paper deals with the fully parabolic 1d chemotaxis system with diffusion 1/(1 + u). We prove that the above mentioned nonlinearity, despite being a natural candidate, is not critical. It means that for such a diffusion any initial condition, independently on the magnitude of mass, generates the global-in-time solution. In view of our theorem one sees that the one-dimensional Keller-Segel system is essentially different from its higher-dimensional versions. In order to prove our theorem we establish a new Lyapunov-like functional associated to the system. The information we gain from our new functional (together with some estimates based on the well-known classical Lyapunov functional) turns out to be rich enough to establish global existence for the initial-boundary value problem. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 146
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 128644802
- Full Text :
- https://doi.org/10.1090/proc/13939