On $L^{\infty }$-estimates and the structure of the global attractor for weak solutions of reaction-diffusion equations
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915821788332032 |
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| author | Caballero, Rubén Kalita, Piotr Valero, José |
| author_facet | Caballero, Rubén Kalita, Piotr Valero, José |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23715 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On $L^{\infty }$-estimates and the structure of the global attractor for weak solutions of reaction-diffusion equations Caballero, Rubén Kalita, Piotr Valero, José Analysis of PDEs Dynamical Systems 35B40, 35B41, 35K55, 37B25, 37B35 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. |
| title | On $L^{\infty }$-estimates and the structure of the global attractor for weak solutions of reaction-diffusion equations |
| topic | Analysis of PDEs Dynamical Systems 35B40, 35B41, 35K55, 37B25, 37B35 |
| url | https://arxiv.org/abs/2602.23715 |