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

• Boudjeriou, Tahir ^[1] ; Kheloufi, Arezki
  1. [1] University of Béjaïa

     University of Béjaïa

     Argelia

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 3, 2022, págs. 579-604
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-3993
• Enlaces
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• Resumen

  • 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.

• Referencias bibliográficas
  • Y. A. Alkhutov, “LP-estimates of solutions of the Dirichlet problem for the heat equation in a ball”, Journal of Mathematical Sciences, vol....
  • M. M. Amangalieva, M. T. Dzhenaliev, M. T. Kosmakova, and M. I. Ramazanov, “On one homogeneous problem for the heat equation in an infinite...
  • V. N. Aref'ev and L. A. Bagirov, “Solutions of the heat equation in domains with singularities”, Mathematical Notes, vol. 64, no. 2, pp....
  • O. V. Besov, “Continuation of functions from Lpl and Wpl” (in Russian), Trudy Mat. Inst. Steklov., vol. 89, pp. 5-17, 1967. [On line]. Available:...
  • M. Chipot and A. Rougirel, “On the asymptotic behaviour of the solution of parabolic problems in cylindrical domains of large size in some...
  • A. S. Fokas and B. Pelloni, “Generalized dirichlet-to-neumann map in time-dependent domains”, Studies in Applied Mathematics, vol. 129, no....
  • S. Guesmia, “Large time and space size behaviour of the heat equation in non-cylindrical domains”, Archiv der Mathematik, vol. 101, no. 3,...
  • S. C. Gupta, “Two-dimensional heat conduction with phase change in a semi-infinite mould”, International Journal of Engineering Science, vol....
  • S. Hofmann and J. L. Lewis, “The Lp Neumann problem for the heat equation in non-cylindrical domains”, Journal of Functional Analysis, vol....
  • A. Kheloufi, R. Labbas, and B.-K. Sadallah, “On the resolution of a parabolic equation in a nonregular domain of ℝ^3”, Differential Equations...
  • A. Kheloufi, “Existence and uniqueness results for parabolic equations with Robin type boundary conditions in a non-regular domain of ℝ3”,...
  • A. Kheloufi and B.-K. Sadallah, “Study of the heat equation in a symmetric conical type domain of ℝN+1”, Mathematical Methods in the Applied...
  • A. Kheloufi, B. K. Sadallah, “Study of a parabolic equation with mixed Dirichlet-Neumann type boundary conditions in unbounded noncylindrical...
  • A. Kheloufi, “On parabolic equations with mixed Dirichlet–Robin type boundary conditions in a non-rectangular domain”, Mediterranean Journal...
  • K. Kuliev and L.-E. Persson, “An extension of Rothe’s method to non-cylindrical domains”, Applications of Mathematics, vol. 52, no. 5, pp....
  • V. V. Kurta and A. E. Shishkov, “Uniqueness classes of solutions of boundary problems for nondivergent second order parabolic equations in...
  • R. Labbas, A. Medeghri, and B.-K. Sadallah, “Sur une équation parabolique dans un domaine non cylindrique”, Comptes Rendus Mathematique, vol....
  • R. Labbas, A. Medeghri, B.-K. Sadallah, “An Lp-approach for the study of degenerate parabolic equations”, Electron. J. Differential Equations,...
  • O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical...
  • Lederman, Claudia, Vazquez, Juan Luis, and Wolanski, Noemi. "A mixed semilinear parabolic problem from combustion theory", Electronic...
  • J. L. Lions, E. Magenes, Problèmes aux Limites Non Homogènes et Applications, vols. 1, 2, Travaux et Recherches Mathématiques Series, vol....
  • F. Paronetto, “An existence result for evolution equations in non-cylindrical domains”, Nonlinear Differential Equations and Applications,...
  • B.-K. Sadallah, “Etude d’un problème 2m-parabolique dans des domaines plan non rectangulaires”, The Bollettino dell'Unione Matematica...
  • B.-K. Sadallah, “Existence de la solution de l'équation de la chaleur dans un disque”, Comptes Rendus de l'Académie des Sciences -...
  • B.-K. Sadallah, “Regularity of a parabolic equation solution in a nonsmooth and unbounded domain,” Journal of the Australian Mathematical...
  • B. K. Sadallah, “A remark on a parabolic problem in a sectorial domain”, Applied Mathematics E-Notes, vol. 8, pp. 263-270, 2008.
  • G. Savaré, “Parabolic problems with mixed variable lateral conditions: An abstract approach”, Journal de Mathématiques Pures et Appliquées,...