, Volume 48, Issue 9, pp 1236-1244

Optimal boundary control of heat transfer in a one-dimensional material: A hyperbolic model

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Abstract

We consider a boundary value problem describing heat propagation in a rod in the framework of a hyperbolic model of heat transfer. We construct a class, depending on a function parameter, of boundary data (controls) ensuring a given rod temperature distribution at a given time; by using the Lagrange method, from this class, we single out a unique control minimizing a given loss function.

Original Russian Text © R.K. Romanovskii, N.G. Churasheva, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 9, pp. 1256–1264.