Existence result for a nonlinear mixed boundary value problem for the heat equation
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913405642735616 |
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| author | Molinarolo, Riccardo |
| author_facet | Molinarolo, Riccardo |
| contents | In this paper we study the existence of solutions in parabolic Schauder space of a nonlinear mixed boundary value problem for the heat equation in a perforated domain. From a given regular open set $Ω\subseteq\mathbb{R}^n$ we remove a cavity $ω\subseteq Ω$. On the exterior boundary of $Ω\setminus\overlineω$ we prescribe a Neumann boundary condition, while on the interior boundary we set a nonlinear Robin-type condition. Under suitable assumptions on the data and by means of Leray Schauder Fixed-Point Theorem, we prove the existence of (at least) one solution $u \in C_{0}^{\frac{1+α}{2}; 1+α}([0,T] \times (\overlineΩ \setminus ω))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18315 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence result for a nonlinear mixed boundary value problem for the heat equation Molinarolo, Riccardo Analysis of PDEs 35K20, 31B10, 47H30, 45A05 In this paper we study the existence of solutions in parabolic Schauder space of a nonlinear mixed boundary value problem for the heat equation in a perforated domain. From a given regular open set $Ω\subseteq\mathbb{R}^n$ we remove a cavity $ω\subseteq Ω$. On the exterior boundary of $Ω\setminus\overlineω$ we prescribe a Neumann boundary condition, while on the interior boundary we set a nonlinear Robin-type condition. Under suitable assumptions on the data and by means of Leray Schauder Fixed-Point Theorem, we prove the existence of (at least) one solution $u \in C_{0}^{\frac{1+α}{2}; 1+α}([0,T] \times (\overlineΩ \setminus ω))$. |
| title | Existence result for a nonlinear mixed boundary value problem for the heat equation |
| topic | Analysis of PDEs 35K20, 31B10, 47H30, 45A05 |
| url | https://arxiv.org/abs/2406.18315 |