Barenblatt solutions for the time-fractional porous medium equation: approach via integral equations
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915409388634112 |
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| author | Caballero, Josefa Okrasińska-Płociniczak, Hanna Płociniczak, Łukasz Sadarangani, Kishin |
| author_facet | Caballero, Josefa Okrasińska-Płociniczak, Hanna Płociniczak, Łukasz Sadarangani, Kishin |
| contents | This paper explores Barenblatt solutions of the time-fractional porous medium equation, characterized by a Caputo-type time derivative. Employing an integral equation approach, we rigorously prove the existence of these solutions and establish several fundamental properties, including upper and lower estimates, mass conservation, regularity, and monotonicity. To bridge theory and practice, we introduce a family of convergent numerical schemes specifically designed to compute the Barenblatt solutions, ensuring reliable and efficient approximations. The theoretical framework is enriched with various examples that illustrate the concepts and validate the effectiveness of the proposed numerical methods, enhancing the understanding and applicability of our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19217 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Barenblatt solutions for the time-fractional porous medium equation: approach via integral equations Caballero, Josefa Okrasińska-Płociniczak, Hanna Płociniczak, Łukasz Sadarangani, Kishin Numerical Analysis Analysis of PDEs This paper explores Barenblatt solutions of the time-fractional porous medium equation, characterized by a Caputo-type time derivative. Employing an integral equation approach, we rigorously prove the existence of these solutions and establish several fundamental properties, including upper and lower estimates, mass conservation, regularity, and monotonicity. To bridge theory and practice, we introduce a family of convergent numerical schemes specifically designed to compute the Barenblatt solutions, ensuring reliable and efficient approximations. The theoretical framework is enriched with various examples that illustrate the concepts and validate the effectiveness of the proposed numerical methods, enhancing the understanding and applicability of our results. |
| title | Barenblatt solutions for the time-fractional porous medium equation: approach via integral equations |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2507.19217 |