rent-now

Rent More, Save More! Use code: ECRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

9783540711285

Beyond Partial Differential Equations : On Linear and Quasi-Linear Abstract Hyperbolic Evolution Equations

by
  • ISBN13:

    9783540711285

  • ISBN10:

    3540711287

  • Format: Paperback
  • Copyright: 2007-06-03
  • Publisher: Springer Verlag
  • Purchase Benefits
List Price: $69.95 Save up to $46.55
  • Digital
    $50.70*
    Add to Cart

    DURATION
    PRICE
    *To support the delivery of the digital material to you, a digital delivery fee of $3.99 will be charged on each digital item.

Summary

The present volume is self-contained and introduces to the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis. Only some examples require more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Particular stress is on equations of the hyperbolic type since considerably less often treated in the literature. Also, evolution equations from fundamental physics need to be compatible with the theory of special relativity and therefore are of hyperbolic type. Throughout, detailed applications are given to hyperbolic partial differential equations occurring in problems of current theoretical physics, in particular to Hermitian hyperbolic systems. This volume is thus also of interest to readers from theoretical physics.

Table of Contents

Conventionsp. 1
Mathematical Introductionp. 5
Quantum Theoryp. 5
Wave Equationsp. 8
Prerequisitesp. 13
Linear Operators in Banach Spacesp. 13
Weak Integration of Banach Space-Valued Mapsp. 25
Exponentials of Bounded Linear Operatorsp. 35
Strongly Continuous Semigroupsp. 41
Elementary Propertiesp. 42
Characterizationsp. 51
An Integral Representation in the Complex Casep. 58
Perturbation Theoremsp. 59
Strongly Continuous Groupsp. 63
Associated Inhomogeneous Initial Value Problemsp. 66
Examples of Generators of Strongly Continuous Semigroupsp. 71
The Ordinary Derivative on a Bounded Intervalp. 71
Linear Stability of Ideal Rotating Couette Flowsp. 74
Outgoing Boundary Conditionsp. 77
Damped Wave Equationsp. 84
Autonomous Linear Hermitian Hyperbolic Systemsp. 97
Intertwining Relations, Operator Homomorphismsp. 105
Semigroups and Their Restrictionsp. 105
Intertwining Relationsp. 114
Nonexpansive Homomorphismsp. 117
Examples of Constrained Systemsp. 123
1-D Wave Equations with Sommerfeld Boundary Conditionsp. 123
1-D Wave Equations with Engquist-Majda Boundary Conditionsp. 127
Maxwell's Equations in Flat Spacep. 132
Kernels, Chains, and Evolution Operatorsp. 137
A Convolution Calculus with Operator-Valued Kernelsp. 138
Chainsp. 146
Juxtaposition of Chainsp. 147
Finitely Generated Chainsp. 148
Evolution Operatorsp. 149
Stable Families of Generatorsp. 155
The Linear Evolution Equationp. 165
Examples of Linear Evolution Equationsp. 177
Scalar Fields in the Gravitational Field of a Spherical Black Holep. 178
Non-Autonomous Linear Hermitian Hyperbolic Systemsp. 199
The Quasi-Linear Evolution Equationp. 215
Examples of Quasi-Linear Evolution Equationsp. 235
A Generalized Inviscid Burgers' Equationp. 235
Quasi-Linear Hermitian Hyperbolic Systemsp. 246
Appendixp. 265
Referencesp. 269
Index of Notationp. 279
Index of Terminologyp. 281
Table of Contents provided by Ingram. All Rights Reserved.

Supplemental Materials

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Rewards Program