| Description |
1 online resource (vii, 216 pages) : illustrations |
| Series |
Inverse and ill-posed problems series, 1381-4524 |
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Inverse and ill-posed problems series. 1381-4524
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| Contents |
Chapter 1. Auxiliary material 1 -- 1.1. Banach spaces and linear operators 1 -- 1.2. Theorems on infinitesimal generators 6 -- 1.3. Functional spaces and differential operators 9 -- Chapter 2. Relatively p-radial operators and degenerate strongly continuous semigroups of operators 13 -- 2.1. Relative resolvents 15 -- 2.2. Relatively p-radial operators 20 -- 2.3. Degenerate strongly continuous semigroups of operators 25 -- 2.4. Approximations of Hille -- Widder -- Post type 31 -- 2.5. Splitting of spaces 36 -- 2.6. Infinitesimal generators and phase spaces 42 -- 2.7. Generators of degenerate strongly continuous semigroups of operators 46 -- 2.8. Degenerate strongly continuous groups of operators 49 -- Chapter 3. Relatively p-sectorial operators and degenerate analytic semigroups of operators 55 -- 3.1. Relatively p-sectorial operators 57 -- 3.2. Degenerate analytic semigroups of operators 59 -- 3.3. Phase spaces for the case of degenerate analytic semigroups 65 -- 3.4. Space splitting 68 -- 3.5. Generators of degenerate analytic semigroups of operators 74 -- 3.6. Degenerate infinitely differentiable semigroups of operators 77 -- 3.7. Phase spaces for the case of degenerate infinitely continuously differentiable semigroups 81 -- 3.8. Kernels and images of degenerate infinitely differentiable semigroups of operators 84 -- Chapter 4. Relatively [sigma]-bounded operators and degenerate analytic groups of operators 87 -- 4.1. Relatively [sigma]-bounded operators 89 -- 4.2. Relative [sigma]-boundedness and relative p-sectoriality 92 -- 4.3. Relative [sigma]-boundedness and relatively adjoint vectors 95 -- 4.4. Degenerate analytical groups of operators 97 -- 4.5. Sufficient conditions of the relative [sigma]-bounded ness 101 -- 4.6. The case of a Fredholm operator 108 -- 4.7. Analytical semigroups of operators degenerating on the chains of relatively adjoint vectors of an arbitrary length 111 -- Chapter 5. Cauchy problem for inhomogeneous Sobolev-type equations 119 -- 5.1. Case of a relatively [sigma]-bounded operator 121 -- 5.2. The case of a relatively p-sectorial operator 131 -- 5.3. Case of a relatively p-radial operator 135 -- 5.4. Strong solution of Cauchy problem 139 -- 5.5. Cauchy problem for an equation with Banach-adjoint operators 143 -- 5.6. Propagators 150 -- 5.7. Inhomogeneous Cauchy problem for high-order Sobolev-type equations 154 -- Chapter 6. Bounded solutions of Sobolev-type equations 159 -- 6.1. Relatively spectral theorem 160 -- 6.2. Bounded relaxed solutions of a homogeneous equation 163 -- 6.3. Bounded solutions of the inhomogeneous equation 170 -- Chapter 7. Optimal control 183 -- 7.1. Strong solution of Cauchy problem for an equation with Hilbert-adjoint operators 183 -- 7.2. Problem of optimal control for an equation with relatively [sigma]-bounded operator 188 -- 7.3. Problem of optimal control for equation with a relatively p-sectorial operator 192 -- 7.4. Barenblatt -- Zheltov -- Kochina equation 194 -- 7.5. System of ordinary differential equations 195 -- 7.6. Equation of the evolution of the free filtered-fluid surface 197 |
| Bibliography |
Includes bibliographical references (pages 201-214) and index |
| Notes |
Print version record |
| Subject |
Sobolev spaces.
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Differential equations, Linear.
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Degenerate differential equations.
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Semigroups of operators.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Degenerate differential equations
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Differential equations, Linear
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Semigroups of operators
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Sobolev spaces
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| Form |
Electronic book
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| Author |
Fedorov, V. E
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| ISBN |
9783110915501 |
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3110915502 |
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