Optimal Control of Nonlinear Evolution Systems in the Case where the Solution is not Differentiable with Respect to the Control

S. Ya. Serovaĭskiĭ

Almaty, Kazakhstan

Abstract: For the simplest heat equation with power nonlinearity, the dependence of the solution of the corresponding boundary-value problem on the constant term of the equation turns out to be, in general, not differentiable in the sense of Gâteaux.

Keywords: optimal control, nonlinear evolution system, heat equation with power nonlinearity, Gâteaux differentiability, Lagrange optimality principle.

UDC: 517.977

Received: 29.02.2012
Revised: 11.09.2012

DOI: 10.4213/mzm4048

 English version: Mathematical Notes, 2013, 93:4, 593–606

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