Abstract Distribution Methods

In this chapter, we consider regularizing operators that allow the construction of an approximate solution stable in https://www.w3.org/1998/Math/MathML" display="inline"> X for concordant parameters: https://www.w3.org/1998/Math/MathML" display="inline"> δ - the error of initial data and the regularization parameter https://www.w3.org/1998/Math/MathML" display="inline"> ε . In Section 4.1, we study three main ‘differential’ regularization methods for an ill-posed Cauchy problem: Lattes-Lions’ quasi-reversibility method, the auxiliary boundary conditions (ABC) method, and the method of reduction to a Dirichlet problem (Carasso’s method). In Section 4.2, we study the connections between different regularization methods and between the regularization methods and the https://www.w3.org/1998/Math/MathML" display="inline"> R -regularized semigroup method.