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1993•Mathematics of the USSR-SbornikRequires access

ON A PROBLEM WITH NONLOCAL BOUNDARY CONDITION FOR A PARABOLIC EQUATION

Л А Муравей, A. V. Filinovskii

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Abstract

Well-posed solvability is proved in an appropriate energy space of a boundary value problem with a nonlocal boundary condition for a one-dimensional parabolic equation; two-sided uniform estimates of the solution are obtained, which replace the maximum principle. The existence of an optimal control of the diffusion coefficient in the problem of minimizing the quality functional is established in the class of functions of bounded variation.

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What this paper is about

Well-posed solvability is proved in an appropriate energy space of a boundary value problem with a nonlocal boundary condition for a one-dimensional parabolic equation; two-sided uniform estimates of the solution are obtained, which replace the maximum principle. The existence of an optimal control of the diffusion coefficient in the problem of minimizing the quality functional is established in the class of functions of bounded variation.

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OpenAlex reports 14 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Well-posed solvability is proved in an appropriate energy space of a boundary value problem with a nonlocal boundary condition for a one-dimensional parabolic equation; two-sided uniform estimates of the solution are obtained, which replace the maximum principle. The existence of an optimal control of the diffusion coefficient in the problem of minimizing the quality functional is established in the class of functions of bounded variation.

Key concepts: Parabolic partial differential equation, Mathematical analysis, Boundary value problem, Heat equation, Mathematics, Physics, Partial differential equation

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