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

khadijeh Baghaei

doi:10.5802/crmath.397

Partial differential equations

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.

Abstract

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.

Received: 2022-03-01
Accepted: 2022-06-12
Published online: 2023-01-12

DOI: 10.5802/crmath.397

Author's affiliations:

khadijeh Baghaei ¹

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

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

@article{CRMATH_2023__361_G1_207_0,
     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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