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This is a Quantitative Study study.

October 12, 2025Open Access

Chemotaxis Models with Nonlinear/Porous Medium Diffusion, Consumption, and Logistic source on RN: I. Global Solvability and Boundedness

Key Points

Global weak solutions exist that remain uniformly bounded over time.
The findings are based on uniform local Lp estimates and continuity arguments.
Moser's iteration technique is used to derive L∞ bounds for these solutions.
The study approaches a parabolic-parabolic chemotaxis system with logistic source terms.

Abstract

This series of papers is concerned with the global solvability, boundedness, regularity, and uniqueness of weak solutions to the following parabolic-parabolic chemotaxis system with a logistic source and chemical consumption: equation* cases uₜ = m ( (+u) ^m-1 u) - χ (u v) + u (a - b u), all of these estimates are uniform as 0. In part II, we will study the regularity and uniqueness of weak solutions.

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