On the Solution of Boundary Value Problems Set in Domains With Moving Boundaries
We construct solutions for time-dependent boundary value problems set in moving domains with Dirichlet, Neumann, and mixed boundary conditions. When the boundaries are time deformations of an initial boundary along a vector field, we can refer the boundary problem to a fixed domain at the cost of in...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/119893 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/119893 |
| Access Level: | acceso abierto |
| Palabra clave: | Boundary value problems Gradient dampings Heat equations Moving boundaries Wave equations Análisis matemático Análisis funcional y teoría de operadores 1202 Análisis y Análisis Funcional |
| Sumario: | We construct solutions for time-dependent boundary value problems set in moving domains with Dirichlet, Neumann, and mixed boundary conditions. When the boundaries are time deformations of an initial boundary along a vector field, we can refer the boundary problem to a fixed domain at the cost of increasing the complexity of the coefficients. This strategy works well for heat equations under general boundary conditions. However, it leads to hyperbolic problems including damping terms of the form ∇ for wave equations, which we are able to solve with zero Dirichlet boundary conditions. For more general boundaries, extension techniques leading to measure valued sources allow us to construct solutions for heat problems with Neumann boundary conditions. |
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