Finite-Time Blowup in a Parabolic-Parabolic-Elliptic Chemotaxis Model Involving Indirect Signal Production

This paper is concerned with a three-component chemotaxis model accounting for indirect signal production, reading as , and , posed in a ball of with , subject to homogeneous Neumann boundary conditions. The system is a Nagai-type variant of its fully parabolic version that has a four-dimensional cr...

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Bibliographic Details
Published inApplied mathematics & optimization Vol. 92; no. 1; p. 10
Main Authors Mao, Xuan, Li, Yuxiang
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2025
Springer Nature B.V
Subjects
Boundary conditions
Calculus of Variations and Optimal Control; Optimization
Control
Differential equations
Energy
Estimates
Explosions
Genotype & phenotype
Inequality
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Simulation
Symmetry
Systems Theory
Theoretical
Indirect signal production
92C17
Finite-time blowup
Primary 35B44
Chemotaxis
Secondary 35K51
35Q92
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Summary:This paper is concerned with a three-component chemotaxis model accounting for indirect signal production, reading as , and , posed in a ball of with , subject to homogeneous Neumann boundary conditions. The system is a Nagai-type variant of its fully parabolic version that has a four-dimensional critical mass phenomenon concerning blowup in finite or infinite time according to the seminal works of Fujie and Senba [J. Differential Equations, 263 (2017), 88–148; 266 (2019), 942–976]. We prove that for any prescribed mass , there exist radially symmetric and positive initial data with such that the corresponding solutions blow up in finite time.
Bibliography:ObjectType-Article-1
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ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-025-10287-x