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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.04326 |
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| _version_ | 1866913640514322432 |
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| author | Liu, Sixuan Dong, Gang Bi, Hui Wu, Boying |
| author_facet | Liu, Sixuan Dong, Gang Bi, Hui Wu, Boying |
| contents | This study investigates Dirichlet boundary condition related to a class of nonlinear parabolic problem with nonnegative $L^1$-data, which has a variable-order fractional $p$-Laplacian operator. The existence and uniqueness of renormalized solutions and entropy solutions to the equation is proved. To address the significant challenges encountered during this process, we use approximation and energy methods. In the process of proving, the well-posedness of weak solutions to the problem has been established initially, while also establishing a comparative result of solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04326 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the solutions to variable-order fractional p-Laplacian evolution equation with L^1-data Liu, Sixuan Dong, Gang Bi, Hui Wu, Boying Analysis of PDEs Primary: 35R11, Secondary: 35D99, 35K67 This study investigates Dirichlet boundary condition related to a class of nonlinear parabolic problem with nonnegative $L^1$-data, which has a variable-order fractional $p$-Laplacian operator. The existence and uniqueness of renormalized solutions and entropy solutions to the equation is proved. To address the significant challenges encountered during this process, we use approximation and energy methods. In the process of proving, the well-posedness of weak solutions to the problem has been established initially, while also establishing a comparative result of solutions. |
| title | On the solutions to variable-order fractional p-Laplacian evolution equation with L^1-data |
| topic | Analysis of PDEs Primary: 35R11, Secondary: 35D99, 35K67 |
| url | https://arxiv.org/abs/2501.04326 |