Tug-of-War games and parabolic problems with spatial and time dependence
In this paper we use probabilistic arguments (Tug-of-War games) to obtain existence of viscosity solutions to a parabolic problem of the form {K(x,t)(Du)ut(x,t)=12⟨D2uJ(x,t)(Du),J(x,t)(Du)(x,t)⟩u(x,t)=F(x)in ΩT,on Γ, where ΩT=Ω×(0,T]ΩT=Ω×(0,T] and ΓΓ is its parabolic boundary. This problem can be vi...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/33121 |
| Acceso en línea: | http://hdl.handle.net/11336/33121 |
| Access Level: | acceso abierto |
| Palabra clave: | Tug-Of-War Parabolic https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | In this paper we use probabilistic arguments (Tug-of-War games) to obtain existence of viscosity solutions to a parabolic problem of the form {K(x,t)(Du)ut(x,t)=12⟨D2uJ(x,t)(Du),J(x,t)(Du)(x,t)⟩u(x,t)=F(x)in ΩT,on Γ, where ΩT=Ω×(0,T]ΩT=Ω×(0,T] and ΓΓ is its parabolic boundary. This problem can be viewed as a version with spatial and time dependence of the evolution problem given by the infinity Laplacian, ut(x,t)=⟨D2u(x,t)Du|Du|(x,t),Du|Du|(x,t)⟩. |
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