Solvability of the mixed initial boundary-value problem for a parabolic equation with a nonlocal condition of first kind
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The spectral method is applied to solve the mixed initial boundary-value problem for a parabolic equation with nonhomogeneous boundary conditions, one of which is nonlocal. We prove existence and uniqueness of the generalized solution of this problem in the Sobolev class W 2 1,0 and represent it as a biorthogonal series. We also consider optimal control by the right-hand side of the equation, which is constructed as a biorthogonal series in the root functions of the spectral problem.
KeywordsBoundary Condition Mathematical Modeling Generalize Solution Computational Mathematic Industrial Mathematic
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