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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.01828 |
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| _version_ | 1866917827799154688 |
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| author | Li, Ying Zhang, Chao |
| author_facet | Li, Ying Zhang, Chao |
| contents | We study the well-posedness of solutions to the general nonlinear parabolic equations with merely integrable data in time-dependent Musielak-Orlicz spaces. With the help of a density argument, we establish the existence and uniqueness of both renormalized and entropy solutions. Moreover, we conclude that the entropy and renormalized solutions for this equation are equivalent. Our results cover a variety of problems, including those with Orlicz growth, variable exponents, and double-phase growth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01828 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Renormalized and entropy solutions to the general nonlinear parabolic equations in Musielak-Orlicz spaces Li, Ying Zhang, Chao Analysis of PDEs We study the well-posedness of solutions to the general nonlinear parabolic equations with merely integrable data in time-dependent Musielak-Orlicz spaces. With the help of a density argument, we establish the existence and uniqueness of both renormalized and entropy solutions. Moreover, we conclude that the entropy and renormalized solutions for this equation are equivalent. Our results cover a variety of problems, including those with Orlicz growth, variable exponents, and double-phase growth. |
| title | Renormalized and entropy solutions to the general nonlinear parabolic equations in Musielak-Orlicz spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.01828 |