Global solutions to semilinear parabolic equations driven by mixed local-nonlocal operators
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911932483633152 |
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| author | Biagi, Stefano Punzo, Fabio Vecchi, Eugenio |
| author_facet | Biagi, Stefano Punzo, Fabio Vecchi, Eugenio |
| contents | We are concerned with the Cauchy problem for the semilinear parabolic equation driven by the mixed local-nonlocal operator $\mathcal{L} = -Δ+(-Δ)^s$, with a power-like source term. We show that the so-called Fujita phenomenon holds, and the critical value is exactly the same as for the fractional Laplacian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17731 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global solutions to semilinear parabolic equations driven by mixed local-nonlocal operators Biagi, Stefano Punzo, Fabio Vecchi, Eugenio Analysis of PDEs We are concerned with the Cauchy problem for the semilinear parabolic equation driven by the mixed local-nonlocal operator $\mathcal{L} = -Δ+(-Δ)^s$, with a power-like source term. We show that the so-called Fujita phenomenon holds, and the critical value is exactly the same as for the fractional Laplacian. |
| title | Global solutions to semilinear parabolic equations driven by mixed local-nonlocal operators |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.17731 |