Existence and Uniqueness of Local and Global Solutions for a Partial Differential-Algebraic Equation of Index One
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911065311281152 |
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| author | Benabdallah, Seyyid Ali Souilah, Messoud |
| author_facet | Benabdallah, Seyyid Ali Souilah, Messoud |
| contents | In this paper, we use the theory of nonlinear semigroups to establish the existence and uniqueness of both local and global solutions for a partial differential-algebraic equation (PDAE) of index one. This method is applied to a reaction-diffusion system coupled with an elliptic equation in one dimension by transforming the PDAE into a system of linear evolution equations with a Lipschitz-continuous perturbation |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15658 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and Uniqueness of Local and Global Solutions for a Partial Differential-Algebraic Equation of Index One Benabdallah, Seyyid Ali Souilah, Messoud Analysis of PDEs 47B01, 47F05, 47H20, 47N60 In this paper, we use the theory of nonlinear semigroups to establish the existence and uniqueness of both local and global solutions for a partial differential-algebraic equation (PDAE) of index one. This method is applied to a reaction-diffusion system coupled with an elliptic equation in one dimension by transforming the PDAE into a system of linear evolution equations with a Lipschitz-continuous perturbation |
| title | Existence and Uniqueness of Local and Global Solutions for a Partial Differential-Algebraic Equation of Index One |
| topic | Analysis of PDEs 47B01, 47F05, 47H20, 47N60 |
| url | https://arxiv.org/abs/2411.15658 |