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Computational Mathematics and Modeling

, Volume 16, Issue 1, pp 72–82 | Cite as

Solvability of the mixed initial boundary-value problem for a parabolic equation with a nonlocal condition of first kind

  • V. V. Tikhomirov
Article
  • 31 Downloads

Abstract

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.

Keywords

Boundary Condition Mathematical Modeling Generalize Solution Computational Mathematic Industrial Mathematic 
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© Springer Science+Business Media, Inc. 2005

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  • V. V. Tikhomirov

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