Regularity and existence for a mixed local-nonlocal parabolic equation with variable singularities and measure data
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916934626312192 |
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| author | Das, Stuti |
| author_facet | Das, Stuti |
| contents | This article proves the existence, non-existence, regularity and asymptotic behavior of weak solutions for a class of mixed local-nonlocal parabolic problems involving singular nonlinearities and measure data extending the works of \cite{sanjitgarain,lazermc}. A central contribution of this work is the inclusion of a variable singular exponent. We examine both the purely singular and perturbed singular cases in the context of measure-valued data, where the source terms can simultaneously take the form of measures. To the best of our knowledge, this phenomenon is new, even in the case of a constant singular exponent involving only a local operator. Further, all our results are also true for the operator being local only. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04797 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularity and existence for a mixed local-nonlocal parabolic equation with variable singularities and measure data Das, Stuti Analysis of PDEs This article proves the existence, non-existence, regularity and asymptotic behavior of weak solutions for a class of mixed local-nonlocal parabolic problems involving singular nonlinearities and measure data extending the works of \cite{sanjitgarain,lazermc}. A central contribution of this work is the inclusion of a variable singular exponent. We examine both the purely singular and perturbed singular cases in the context of measure-valued data, where the source terms can simultaneously take the form of measures. To the best of our knowledge, this phenomenon is new, even in the case of a constant singular exponent involving only a local operator. Further, all our results are also true for the operator being local only. |
| title | Regularity and existence for a mixed local-nonlocal parabolic equation with variable singularities and measure data |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.04797 |