Blow-up of nonradial solutions to the hyperbolic-elliptic chemotaxis system with logistic source

khadijeh Baghaei

doi:10.5802/crmath.397

Équations aux dérivées partielles

Blow-up of nonradial solutions to the hyperbolic-elliptic chemotaxis system with logistic source

khadijeh Baghaei ¹

¹ School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 207-215.

Résumé

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

\{\begin{matrix} u_{t} = - \nabla \cdot (χ u \nabla v) + g (u), x \in Ω, t > 0, \\ 0 = Δ v - v + u, x \in Ω, t > 0, \end{matrix}

under homogeneous Neumann boundary conditions in a bounded domain $Ω \subset ℝ^{n}, n \geq 1,$ with smooth boundary and the function $g$ is assumed to generalize the logistic source:

g (s) \leq a s - b s^{γ} for s > 0

with $1 < γ \leq 2 .$ 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.

Reçu le : 2022-03-01
Accepté le : 2022-06-12
Publié le : 2023-01-12

DOI : 10.5802/crmath.397

Affiliations des auteurs :

khadijeh Baghaei 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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     author = {khadijeh Baghaei},
     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},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.397},
     language = {en},
}

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khadijeh Baghaei. Blow-up of nonradial solutions to the hyperbolic-elliptic chemotaxis system with logistic source. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 207-215. doi : 10.5802/crmath.397. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.397/

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