On the third boundary value problem for parabolic equations in a non-regular domain of Rᴺ +1
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CitationKheloufi, A. (2016). On the third boundary value problem for parabolic equations in a non-regular domain OFRN +1. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, 6(1), 1-14.
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 , to the case where the domain is cylindrical, not with respect to the time variable, but with respect to N space variables, N > 1.
SourceTWMS Journal of Applied and Engineering Mathematics