Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898686 | Journal of Differential Equations | 2018 | 19 Pages |
Abstract
We consider a second order PDEs system of Parabolic-Elliptic type with chemotactic terms. The system describes the evolution of a biological species “u” moving towards a higher concentration of a chemical stimuli “v” in a bounded and open domain of RN. In the system considered, the chemotaxis sensitivity depends on the gradient of v, i.e., the chemotaxis term has the following expressionâdiv(Ïu|âv|pâ2âv), where Ï is a positive constant and p satisfiespâ(1,â), if N=1 and pâ(1,NNâ1), if Nâ¥2. We obtain uniform bounds in Lâ(Ω) and the existence of global in time solutions. For the one-dimensional case we prove the existence of infinitely many non-constant steady-states for pâ(1,2) for any Ï positive and a given positive mass.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Mihaela Negreanu, J. Ignacio Tello,