Linear Sobolev Type Equations and Degenerate Semigroups of Operators.

Intro -- 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 Hille-Widder-Post 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 σ-bounded operators and degenerate analytic groups of operators -- 4.0. Introduction -- 4.1. Relatively σ-bounded operators -- 4.2. Relative σ-boundedness and relative p-sectoriality -- 4.3. Relative σ-boundedness and relatively adjoint vectors -- 4.4. Degenerate analytical groups of operators -- 4.5. Sufficient conditions of the relative σ-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. Barenblatt-Zheltov-Kochina equation -- 7.5. System of ordinary differential equations -- 7.6. Equation of the evolution of the free filtered-fluid surface -- Bibliography -- Index.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.