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

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 $L^{\infty} (Ω)$ . 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.

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

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

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On L∞L∞-estimates and the structure of the global attractor for weak solutions of reaction-diffusion equations

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On L∞L∞-estimates and the structure of the global attractor for weak solutions of reaction-diffusion equations

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

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AI智能校验

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

讲解博客

AI智能校验