DOI: https://doi.org/10.26089/NumMet.v22r417

On boundary optimal control of a coefficient in a nonlinear parabolic equation

Authors

  • Nataliya L. Gol’dman

Keywords:

parabolic equations
optimal control with final observation
conjugate problem
applications for physical-chemical processes

Abstract

The work is connected with investigation of nonlinear parabolic systems arising in the mathematical modeling and control of physical-chemical processes in which inner properties of materials are subjected to changes. We consider optimal control in one of such systems that involves a boundary value problem of the third kind for a quasilinear parabolic equation with an unknown coefficient at the time derivative and, moreover, an additional equation for a time dependence of this coefficient. The optimal problem with a boundary control regime is justified for the given final observation of the sought coefficient. The exact representation for the differential of the minimization functional in terms of the solutions of the conjugate problem is obtained. The form of this conjugate problem and conditions of unique solvability in a class of smooth functions are shown. The obtained results are important for applications in various technical fields, medicine, geology, etc. Some examples of such applications are discussed.

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Published

2021-11-10

Issue

Vol. 22 (2021): Issue 4.

Section

Methods and algorithms of computational mathematics and their applications

Author Biography

Nataliya L. Gol’dman

Lomonosov Moscow State University,
Research Computing Center
• Leading Researcher

References

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