Heat equations with fast convection: Source-type solutions and large-time behaviour

We study the existence and uniqueness of source-type solutions to the Cauchy problem for the heat equation with fast convection under certain tail control assumptions. We allow the solutions to change sign, but we will in fact show that they have the same sign as the initial data, which is a multipl...

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Detalles Bibliográficos
Autores: Endal, Jørgen, Ignat, Liviu I., Quirós Gracián, Fernando
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/746160
Acceso en línea:https://hdl.handle.net/10486/746160
https://dx.doi.org/10.3934/dcdss.2023182
Access Level:acceso abierto
Palabra clave:Diffusion-convection
fast convection
source-type solutions
uniqueness
asymptotic behaviour
Matemáticas
Descripción
Sumario:We study the existence and uniqueness of source-type solutions to the Cauchy problem for the heat equation with fast convection under certain tail control assumptions. We allow the solutions to change sign, but we will in fact show that they have the same sign as the initial data, which is a multiple of the Dirac delta. As an application, we obtain the large-time behaviour of nonnegative bounded solutions with integrable initial data to heat equations with fast convection, covering the case of several dimensions that remained open since the end of last century