On the Solvability of an Evolution Problem with Weighted Integral Boundary Conditions in Sobolev Function Spaces with a Priori Estimate and Fourier’s Method
DJIBIBE Moussa Zakari *
University of Lom´ e, Department of Mathematics PO Box 1515 Lom´ e, Togo.
TCHARIE Kokou
University of Lom´ e, Department of Mathematics PO Box 1515 Lom´ e, Togo.
*Author to whom correspondence should be addressed.
Abstract
Aims/ The aims of this paper are to prove existence and uniqueness of following integral boundary
conditions mixed problem for parabolic equation :
The proofs are based on a priori estimates established in Sobolev function spaces and Fourier’s
method.
Keywords: Fourier’s method, A priori Estimate, Nonlocal conditions, Mixed Problem, Parabolic Equation, Sobolev Espace