The Global Existence and Boundedness of Solutions to a Chemotaxis–Haptotaxis Model with Nonlinear Diffusion and Signal Production

Beibei Ai and Zhe Jia ()
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Beibei Ai: School of Mathematics and Statistics, Linyi University, Linyi 276005, China
Zhe Jia: School of Mathematics and Statistics, Linyi University, Linyi 276005, China

Mathematics, 2024, vol. 12, issue 16, 1-11

Abstract: In this paper, we investigate the following chemotaxis–haptotaxis system (1) with nonlinear diffusion and signal production under homogenous Neumann boundary conditions in a bounded domain with smooth boundary. Under suitable conditions on the data we prove the following: (i) For 0 < γ ≤ 2 n , if α > γ − k + 1 and β > 1 − k , problem (1) admits a classical solution ( u , v , w ) which is globally bounded. (ii) For 2 n < γ ≤ 1 , if α > γ − k + 1 e + 1 and β > max { ( n γ − 2 ) ( n γ + 2 k − 2 ) 2 n − k + 1 , ( n γ − 2 ) ( γ + 1 e ) n − k + 1 } or α > γ − k + 1 and β > max { ( n γ − 2 ) ( n γ + 2 k − 2 ) 2 n − k + 1 , ( n γ − 2 ) ( α + k − 1 ) n − k + 1 } , problem (1) admits a classical solution ( u , v , w ) which is globally bounded.

Keywords: boundedness; chemotaxis–haptotaxis; nonlinear diffusion; signal production (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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