In this paper, we study an alarm–taxis system with nonlinear diffusion $\Delta {w}&#x0005E;m\left(m&gt;1\right)$ . We consider this problem in a bounded domain $\Omega \subset {\mathbb{R}}&#x0005E;N\left(N\ge 1\right)$ with Neumann boundary conditions. By the complex coupling energy estimates based on the Neumann semigroup smoothing properties, we establish the existence of globally bounded weak solutions for any $m&gt;1$ .

Conflicts of Interest

The authors declare no conflicts of interest.

Open Research

Data Availability Statement

The authors have nothing to report.

References

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Volume48, Issue12

August 2025

Pages 12085-12099

Global Boundedness of an Alarm–Taxis System With Nonlinear Diffusion

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Global Boundedness of an Alarm–Taxis System With Nonlinear Diffusion

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