On $L^{\infty }$-estimates and the structure of the global attractor for weak solutions of reaction-diffusion equations

Rubén Caballero; Piotr Kalita; José Valero

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arXiv · 2602.23715

On $L^{\infty }$-estimates and the structure of the global attractor for weak solutions of reaction-diffusion equations

Rubén Caballero·Piotr Kalita·José Valero

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Abstract

In this paper, we study the structure of the global attractor for weak and regular solutions of a problem governed by a scalar semilinear reaction-diffusion equation with a non-regular nonlinearity, such that uniquness of solutions can fail to happen. First, using the Moser--Alikakos iterations we obtain the estimates of the weak solutions in the space $L^{\infty }(\Omega)$. After that, using these estimates we improve the existing results on the structure of the attractor. Finally, estimates of the Hausdorff and fractal dimension of the attractor are obtained.

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Rubén Caballero, Piotr Kalita, José Valero. 2026-02-27. On $L^{\infty }$-estimates and the structure of the global attractor for weak solutions of reaction-diffusion equations. https://arxiv.org/abs/2602.23715

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