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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.15618 |
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| _version_ | 1866918509937688576 |
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| author | Kametaka, Mikiya Kawakami, Tatsuki |
| author_facet | Kametaka, Mikiya Kawakami, Tatsuki |
| contents | We establish the global existence and uniqueness of $L^1$-solutions to the Cauchy problem for time-fractional porous medium type nonlinear diffusion equations. Furthermore, we give the mass conservation law for $L^1$-solutions to time-fractional fast diffusion equations, and prove that the finite-time extinction does not occur for any nonnegative $L^1$-solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15618 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence and uniqueness of $L^1$-solutions to time-fractional nonlinear diffusion equations Kametaka, Mikiya Kawakami, Tatsuki Analysis of PDEs We establish the global existence and uniqueness of $L^1$-solutions to the Cauchy problem for time-fractional porous medium type nonlinear diffusion equations. Furthermore, we give the mass conservation law for $L^1$-solutions to time-fractional fast diffusion equations, and prove that the finite-time extinction does not occur for any nonnegative $L^1$-solutions. |
| title | Existence and uniqueness of $L^1$-solutions to time-fractional nonlinear diffusion equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.15618 |