/ Inv. Ill-Posed Problems, Vol.3, No.3, pp.249-257 (1995) © VSP 1995 J. JANNO* and L.v.WOLFERSDORFt Received December 12, 1994 Abstract -- A method of regularization of a class of nonlinear Volterra equations of a convolution type is analysed. The equations arise when solving inverse problems of determining the memory kernels in a heat flow. 1. INTRODUCTION In  we reduce a class of inverse problems of identifying the memory kernels in a heat flow to integral equations of the type: K0m(t) = I* K[m](t - s)m(s)ds = /(t) , 0< t C[0,T]}. Under suitable conditions imposed on the data of the inverse problems there exists an integer n > l such that (1.1) becomes an equation of the second kind after we differentiate it n times. The integral operator KQ is -smoothing, i.e. K^rn G Cn[0, T] if m £ C[0, T]. On the other hand, in applications the function /, which contains the observation data of the problem, is given approximately in 6[0, ]. Since the problem is ill-posed in this space, we must apply regularization techniques. In this paper we consider the general equation (1.1) with the above properties. We denote by fs the approximation of
Journal of Inverse and Ill-Posed Problems – de Gruyter
Published: Jan 1, 1995
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