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Global existence of solutions to a fully parabolic chemotaxis system with singular sensitivity and logistic source.
- Source :
-
Nonlinear Analysis: Real World Applications . Oct2019, Vol. 49, p286-311. 26p. - Publication Year :
- 2019
-
Abstract
- In this paper we study the global existence of solutions to the fully parabolic chemotaxis system: u t = Δ u − χ ∇ ⋅ (u v ∇ v) + f (u) , v t = Δ v − v + u in a smooth bounded domain Ω ⊂ R n (n ≥ 3) subject to the non-flux boundary conditions, where χ > 0 and the logistic function f ∈ C 1 [ 0 , ∞) satisfies f (s) ≤ r − μ s γ with r ≥ 0 and γ , μ > 0. It is shown that the problem possesses a global and classical solution as long as γ > 2. Moreover, the global existence of the weak solution is also established provided that f (s) = r s − μ s 2 with any r , μ > 0. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CHEMOTAXIS
*PARABOLIC operators
*BLOWING up (Algebraic geometry)
*GLOBAL studies
Subjects
Details
- Language :
- English
- ISSN :
- 14681218
- Volume :
- 49
- Database :
- Academic Search Index
- Journal :
- Nonlinear Analysis: Real World Applications
- Publication Type :
- Academic Journal
- Accession number :
- 136349787
- Full Text :
- https://doi.org/10.1016/j.nonrwa.2019.03.009