MR
Yu. F. DOLGII and P. G. SURKOV
Yu. F. DOLGII and P. G. SURKOV
A Variational Approach towards Solving an Ill-Posed Cauchy Problem for a Functional-Differential Equation
Funkcialaj Ekvacioj. Serio Internacia
59
2016
157--183
http://fe.math.kobe-u.ac.jp/FE/FullPapers/59-2/59_157.pdf
http://www.ams.org/mathscinet-getitem?mr=MR
We investigate an ill-posed Cauchy problem for a linear functional-differential equation of retarded type on the negative half-line. Using a step-by-step procedure this problem is replaced by an inverse problem for an operator equation of the first kind in a functional space. The Tikhonov's method is then used for finding solutions. We also construct special boundary value problems for the functional-differential equations. Solutions of these boundary value problems determine regularized solutions of the ill-posed Cauchy problem by the step-by-step procedure.
Linear functional differential equation, Ill-posed problems.
34K06, 47A52.
59-157
2016
A Variational Approach towards Solving an Ill-Posed Cauchy Problem for a Functional-Differential Equation
Yu. F. DOLGII and P. G. SURKOV
Yu. F. DOLGII and P. G. SURKOV
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