What is included with this book?
Preface | p. v |
Dissipative and Maximal Monotone Operators | p. 1 |
Duality mapping and directional derivatives of norms | p. 1 |
Dissipative operators | p. 9 |
Properties of m-dissipative operators | p. 17 |
Perturbation results for m-dissipative operators | p. 25 |
Maximal monotone operators | p. 32 |
Convex functionals and subdifferentials | p. 40 |
Linear Semigroups | p. 57 |
Examples and basic definitions | p. 57 |
Cauchy problems and mild solutions | p. 66 |
The Hille-Yosida theorem | p. 74 |
The Lumer-Phillips theorem | p. 79 |
A second order equation | p. 83 |
Analytic Semigroups | p. 89 |
Dissipative operators and sesquilinear forms | p. 89 |
Analytic semigroups | p. 97 |
Approximation of C[subscript 0]-Semigroups | p. 115 |
The Trotter-Kato theorem | p. 115 |
Approximation of nonhomogeneous problems | p. 131 |
Variational formulations of the Trotter-Kato theorem | p. 135 |
An approximation result for analytic semigroups | p. 141 |
Nonlinear Semigroups of Contractions | p. 147 |
Generation of nonlinear semigroups | p. 147 |
Cauchy problems with dissipative operators | p. 153 |
The infinitesimal generator | p. 163 |
Nonlinear diffusion | p. 175 |
Locally Quasi-Dissipative Evolution Equations | p. 181 |
Locally quasi-dissipative operators | p. 183 |
Assumptions on the operators A(t) | p. 186 |
DS-approximations and fundamental estimates | p. 188 |
Existence of DS-approximations | p. 202 |
Existence and uniqueness of mild solutions | p. 208 |
Autonomous problems | p. 229 |
"Nonhomogeneous" problems | p. 231 |
Strong solutions | p. 238 |
Quasi-linear equations | p. 246 |
A "parabolic" problem | p. 253 |
The Crandall-Pazy Class | p. 263 |
The conditions | p. 263 |
Existence of an evolution operator | p. 267 |
Variational Formulations and Gelfand Triples | p. 285 |
Cauchy problems and Gelfand triples | p. 285 |
An approximation result | p. 301 |
Applications to Concrete Systems | p. 305 |
Delay-differential equations | p. 305 |
Equations of retarded type in the state space C | p. 306 |
State dependent delays | p. 313 |
Equations of neutral type | p. 319 |
Scalar conservation laws | p. 326 |
Basic assumptions and preliminaries | p. 326 |
Globally bounded functions | p. 331 |
Vanishing viscosity, quasi-dissipativity | p. 333 |
L[superscript 2]-considerations | p. 338 |
L[superscript 1]- and L[superscript [infinity]-estimates | p. 342 |
W[superscript 1,1]-estimates | p. 347 |
Uniformity with respect to v | p. 354 |
The limit v [characters not reproducible] 0 | p. 361 |
The limiting operator | p. 378 |
The general case | p. 385 |
The Navier-Stokes equations | p. 386 |
The two-dimensional case | p. 398 |
The three-dimensional case | p. 403 |
Approximation of Solutions for Evolution Equations | p. 409 |
Approximation by approximating evolution problems | p. 409 |
Chernoff's theorem | p. 427 |
Operator splitting | p. 440 |
Semilinear Evolution Equations | p. 447 |
Well-posedness | p. 447 |
Delay equations with time and state dependent delays | p. 458 |
Approximation theory | p. 463 |
A concrete approximation scheme for delay systems | p. 469 |
Appendix | p. 479 |
Some inequalities | p. 479 |
Convergence of Steklov means | p. 483 |
Some technical results needed in Section 9.2 | p. 484 |
Bibliography | p. 489 |
List of Symbols | p. 493 |
Index | p. 495 |
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