Quasi-linear parabolic equations having a superlinear gradient term which depends on the solution
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909688560353280 |
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| author | Dall'Aglio, Andrea Magliocca, Martina de León, Sergio Segura |
| author_facet | Dall'Aglio, Andrea Magliocca, Martina de León, Sergio Segura |
| contents | In this paper, we study existence and regularity for solutions to parabolic equations having a superlinear lower order term depending on both the solution and its gradient. Two different situations are analyzed. On the one hand, we assume that the initial datum belongs to an Orlicz space of exponentially summable functions. On the other, data in an appropriate Lebesgue space satisfying a smallness condition are considered. Our results are coherent with those of previous papers in similar frameworks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09978 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-linear parabolic equations having a superlinear gradient term which depends on the solution Dall'Aglio, Andrea Magliocca, Martina de León, Sergio Segura Analysis of PDEs In this paper, we study existence and regularity for solutions to parabolic equations having a superlinear lower order term depending on both the solution and its gradient. Two different situations are analyzed. On the one hand, we assume that the initial datum belongs to an Orlicz space of exponentially summable functions. On the other, data in an appropriate Lebesgue space satisfying a smallness condition are considered. Our results are coherent with those of previous papers in similar frameworks. |
| title | Quasi-linear parabolic equations having a superlinear gradient term which depends on the solution |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.09978 |