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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.41 no.3 Antofagasta June 2022 


On the resolution of the heat equation in unbounded non-regular domains of R³

Tahir Boudjeriou1 

Arezki Khelouf2 

1Laboratoire de Mathématiques Appliquées, Département des Mathématiques, Faculté des Sciences Exactes, Université de Bejaia, 06000 Bejaia, Algérie. e-mail:

2Department of Technology, Faculty of Technology, Lab. of Applied Mathematics, Bejaia University, 06000 Bejaia, Algeria. e-mail:


We will prove well posedness and regularity results for the bidimensional heat equation, subject to mixed Dirichlet-Neumann type boundary conditions on the parabolic boundary of an unbounded (in one space variable direction) time-dependent domain. Our results are proved in anisotropic Hilbertian Sobolev spaces by using the domain decomposition method. This work complements the results obtained in [13] in the one-space variable case.

Keywords: heat equation; unbounded non-regular domains; Dirichlet-Neumann condition; anisotropic Sobolev spaces

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Received: February 28, 2020; Accepted: December 30, 2021

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