Journal of Siberian Federal University. Mathematics & Physics: Global in Space Regularity Results for the Heat Equation with Robin-Neumann Type Boundary Conditions in Time-varying Domains

Journal of Siberian Federal University. Mathematics & Physics / Global in Space Regularity Results for the Heat Equation with Robin-Neumann Type Boundary Conditions in Time-varying Domains

Issue: Journal of Siberian Federal University. Mathematics & Physics. 2019 12 (3)
Authors: Boudjeriou, Tahir; Kheloufi, Arezki
Contact information: Boudjeriou, Tahir: Laboratory of Applied Mathematics, Department of Mathematics Faculty of Exact Sciences, University of Bejaia, Bejaia, 6000 Algeria; ; Kheloufi, Arezki: Department of Technology, Faculty of Technology Lab. of Applied Mathematics, Bejaia University, Bejaia, 6000 Algeria; ,
Keywords: heat equation; Unbounded non-cylindrical domains; Robin condition; Neumann condition; anisotropic Sobolev spaces
Abstract: This article deals with the heat equation @tu @2x u = f in D; D = {(t; x) 2 R2 : a < t < b; (t) < x < +1} with the function satisfying some conditions and the problem is supplemented with boundary conditions of Robin-Neumann type. We study the global regularity problem in a suitable parabolic Sobolev space. We prove in particular that for f 2 L2(D) there exists a unique solution u such that u; @tu; @jx u 2 L2 (D) ; j = 1; 2: The proof is based on the domain decomposition method. This work complements the results obtained in [10].
Pages: 355–370
DOI: 10.17516/1997-1397-2019-12-3-355-370
Paper at repository of SibFU: https://elib.sfu-kras.ru/handle/2311/110283