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Blow-up of nonradial solutions to the hyperbolic-elliptic chemotaxis system with logistic source
Baghaei, khadijeh1 
1 School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran
Comptes Rendus. Mathématique, Tome 361 (2023) no. G1, pp. 207-215

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This paper is concerned with the blow-up of solutions to the following hyperbolic-elliptic chemotaxis system:

u t =-∇·(χu∇v)+g(u),x∈Ω,t>0,0=Δv-v+u,x∈Ω,t>0,

under homogeneous Neumann boundary conditions in a bounded domain Ω⊂ℝ n ,n≥1, with smooth boundary and the function g is assumed to generalize the logistic source:

g(s)≤as-bs γ fors>0

with 1<γ≤2. For b<χ and some suitable conditions on parameters of problem, we prove that the solutions of this problem blow up in finite time. This result extend the obtained results for this problem.

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Accepté le :
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DOI : 10.5802/crmath.397

Baghaei, khadijeh 1

1 School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Blow-up of nonradial solutions to the hyperbolic-elliptic chemotaxis system with logistic source},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {207--215},
     publisher = {Acad\'emie des sciences, Paris},
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     year = {2023},
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Baghaei, khadijeh. Blow-up of nonradial solutions to the hyperbolic-elliptic chemotaxis system with logistic source. Comptes Rendus. Mathématique, Tome 361 (2023) no. G1, pp. 207-215. doi: 10.5802/crmath.397

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