Global Existence and Boundedness of Gray-Scott Model with Local and Nonlocal Diffusion
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908583164116992 |
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| author | Alam, Md Shah |
| author_facet | Alam, Md Shah |
| contents | In this paper, we study the global existence of component-wise nonnegative solutions of the Gray-Scott model in $Ω\subset \mathbb{R}^n$, $n \ge 1$, with a mixture of both local and nonlocal diffusion operators. We use semigroup theory with duality arguments to establish the global existence and boundedness of solutions of our model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15535 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Existence and Boundedness of Gray-Scott Model with Local and Nonlocal Diffusion Alam, Md Shah Analysis of PDEs In this paper, we study the global existence of component-wise nonnegative solutions of the Gray-Scott model in $Ω\subset \mathbb{R}^n$, $n \ge 1$, with a mixture of both local and nonlocal diffusion operators. We use semigroup theory with duality arguments to establish the global existence and boundedness of solutions of our model. |
| title | Global Existence and Boundedness of Gray-Scott Model with Local and Nonlocal Diffusion |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.15535 |