Linear Sobolev Type Equations and Degenerate Semigroups of Operators (Inverse and Ill-Posed Problems) 9067643831, 9789067643832

Table of contents :
Chapter 1. Auxiliary material
1.1. Banach spaces and linear operators
1.2. Theorems on infinitesimal generators
1.3. Functional spaces and differential operators
Chapter 2. Relatively p-radial operators and degenerate strongly continuous semigroups of operators
2.0. Introduction
2.1. Relative resolvents
2.2. Relatively p-radial operators
2.3. Degenerate strongly continuous semigroups of operators
2.4. Approximations of HilleWidderPost type
2.5. Splitting of spaces
2.6. Infinitesimal generators and phase spaces
2.7. Generators of degenerate strongly continuous semigroups of operators
2.8. Degenerate strongly continuous groups of operators
Chapter 3. Relatively p-sectorial operators and degenerate analytic semigroups of operators
3.0. Introduction
3.1. Relatively p-sectorial operators
3.2. Degenerate analytic semigroups of operators
3.3. Phase spaces for the case of degenerate analytic semigroups
3.4. Space splitting
3.5. Generators of degenerate analytic semigroups of operators
3.6. Degenerate infinitely differentiable semigroups of operators
3.7. Phase spaces for the case of degenerate infinitely continuously differentiable semigroups
3.8. Kernels and images of degenerate infinitely differentiable semigroups of operators
Chapter 4. Relatively .-bounded operators and degenerate analytic groups of operators
4.0. Introduction
4.1. Relatively .-bounded operators
4.2. Relative .-boundedness and relative p-sectoriality
4.3. Relative .-boundedness and relatively adjoint vectors
4.4. Degenerate analytical groups of operators
4.5. Sufficient conditions of the relative .-bounded ness
4.6. The case of a Fredholm operator
4.7. Analytical semigroups of operators degenerating on the chains of relatively adjoint vectors of an arbitrary length
Chapter 5. Cauchy problem for inhomogeneous Sobolev-type equations
5.0. Introduction
5.1. Case of a relatively s-bounded operator
5.2. The case of a relatively p-sectorial operator
5.3. Case of a relatively p-radial operator
5.4. Strong solution of Cauchy problem
5.5. Cauchy problem for an equation with Banach-adjoint operators
5.6. Propagators
5.7. Inhomogeneous Cauchy problem for high-order Sobolev-type equations
Chapter 6. Bounded solutions of Sobolev-type equations
6.0. Introduction
6.1. Relatively spectral theorem
6.2. Bounded relaxed solutions of a homogeneous equation
6.3. Bounded solutions of the inhomogeneous equation
6.4. Examples
Chapter 7. Optimal control
7.0. Introduction
7.1. Strong solution of Cauchy problem for an equation with Hilbert-adjoint operators
7.2. Problem of optimal control for an equation with relatively s-bounded operator
7.3. Problem of optimal control for equation with a relatively p-sectorial operator
7.4. BarenblattZheltovKochina equation
7.5. System of ordinary differential equations
7.6. Equation of the evolution of the free filtered-fluid surface
Bibliography
Index