Dergiler / TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics / 2016 / Cilt: 6 - Sayı: 1

ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OFRN +1

Arezkı KHELOUFI

Sayfa
1–14
DOI
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Abstract

In this paper, we look for sufficient conditions on the lateral surface ofthe domain and on the coefficients of the boundary conditions of a N-space dimensionallinear parabolic equation, in order to obtain existence, uniqueness and maximal regularityof the solution in a Hilbertian anisotropic Sobolev space when the right hand side of theequation is in a Lebesgue space. This work is an extension of solvability results obtainedfor a second order parabolic equation, set in a non-regular domain ofR3obtained in [1],to the case where the domain is cylindrical, not with respect to the time variable, butwith respect to N space variables, N > 1

ON THE THIRD BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS IN A NON-REGULAR DOMAIN OFRN +1 — AJindex