Title of article :
ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OF RN+1
Author/Authors :
KHELOUFI, AREZKI Laboratoire de Math´ematiques Appliqu´ees - Facult´e des Sciences Exactes - Universit´e de Bejaia - Bejaia - Alg´erie. Lab. E.D.P.N.L. and Hist. of Maths - Ecole Normale Sup´erieure -Kouba - Algiers, Algeria
Abstract :
Abstract. In this paper, we look for sufficient conditions on the lateral surface of
the domain and on the coefficients of the boundary conditions of a N−space dimensional
linear parabolic equation, in order to obtain existence, uniqueness and maximal regularity
of the solution in a Hilbertian anisotropic Sobolev space when the right hand side of the
equation is in a Lebesgue space. This work is an extension of solvability results obtained
for a second order parabolic equation, set in a non-regular domain of R
3
obtained in [1],
to the case where the domain is cylindrical, not with respect to the time variable, but
with respect to N space variables, N > 1.
Keywords :
Parabolic equations , Non-regular domains , Robin conditions , Anisotropic Sobolev spaces
Journal title :
Turkish World Mathematical Society Journal of Applied and Engineering Mathematics
