On the estimate of accuracy of the auxiliary boundary conditions method for solving a boundary value inverse problem for a nonlinear equation
E.V. Tabarintseva
South Ural State University, Chelyabinsk, prosp. Lenina, 76, Russia, 454080
Keywords: параболическое уравнение, обратная задача, модуль непрерывности обратного оператора, метод приближенного решения, оценка погрешности, parabolic equation, inverse problem, modulus of continuity of the inverse operator, approximate method, error estimate
Abstract
An inverse boundary value problem for a nonlinear parabolic equation is considered. Two-way estimates for the norms of values of a nonlinear operator in terms of the norms of values of the corresponding linear operator are obtained. Consequent by the two-way estimates are established for the modulus of continuity of a nonlinear inverse problem in terms of the modulus of continuity of the corresponding linear problem. The auxiliary boundary conditions method to construct stable approximate solutions to the nonlinear inverse problem is used. An accurate in order error estimate for the auxiliary boundary conditions method on a uniform regularization class has been obtained.
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