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Proyecciones (Antofagasta)

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BOUDJERIOU, Tahir  and  KHELOUF, Arezki. On the resolution of the heat equation in unbounded non-regular domains of R³. Proyecciones (Antofagasta) [online]. 2022, vol.41, n.3, pp.579-604. ISSN 0716-0917.

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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