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2) 2 Analysis of Statements and Solution Methods 36 The initial temperature distribution is known as T(x,O) = cp(x), At the point x 0 ~ x ~ b. 4) O~T~Tm. 5) where A, = const > O. The determination of the heat flux on the left boundary q(T) = - A,oT(O, T)/OX is required. e. the stability of the given problem, assuming that the existence and uniqueness of solution have taken place. As a preliminary, let us specify the computational statements of the boundary IHCP. For this, take three possible cases: a boundary-value statement, a statement in the Cauchy form, and a variational statement of the problem [12].
1 Inverse Problems Formulation and Stability of Their Solution 3S a description of the general regularization method suggested by Tikhonov which can be applied to a solution of a wide range of problems. One of its major varieties - a variational method - is specially outlined. It is also pointed out that lately a new regularization method - an iterative regularization - has been considerably developed and found practical application as elaborated upon by the author and his colleagues. 1 General Mathematical Formulation The general statement of inverse heat transfer problems has been introduced in Sect.
Recently methods to determine the thermophysical properties of materials became widespread: they are based on solving coefficient inverse problems. This fact is accounted for by the superiority of this approach over the traditional methods of measuring thermophysical properties, especially in studying properties over wide temperature ranges, at large velocities and temperature change gradients, and in the presence of phase transitions within the material. For example, among the problems that are of great practical importance are those to determine the temperature dependence of thermal conductivity and temperature field of a cooled ingot during steel tempering.
Fluid Thermal Processes - Systems Analysis, Control
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