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Conventions 1
Mathematical Introduction 5
Quantum Theory 5
Wave Equations 8
Prerequisites 13
Linear Operators in Banach Spaces 13
Weak Integration of Banach Space-Valued Maps 25
Exponentials of Bounded Linear Operators 35
Strongly Continuous Semigroups 41
Elementary Properties 42
Characterizations 51
An Integral Representation in the Complex Case 58
Perturbation Theorems 59
Strongly Continuous Groups 63
Associated Inhomogeneous Initial Value Problems 66
Examples of Generators of Strongly Continuous Semigroups 71
The Ordinary Derivative on a Bounded Interval 71
Linear Stability of Ideal Rotating Couette Flows 74
Outgoing Boundary Conditions 77
Damped Wave Equations 84
Autonomous Linear Hermitian Hyperbolic Systems 97
Intertwining Relations, Operator Homomorphisms 105
Semigroups and Their Restrictions 105
Intertwining Relations 114
Nonexpansive Homomorphisms 117
Examples of Constrained Systems 123
1-D Wave Equations with Sommerfeld Boundary Conditions 123
1-D Wave Equations with Engquist-Majda Boundary Conditions 127
Maxwell's Equations in Flat Space 132
Kernels, Chains, and Evolution Operators 137
A Convolution Calculus with Operator-Valued Kernels 138
Chains 146
Juxtaposition of Chains 147
Finitely Generated Chains 148
Evolution Operators 149
Stable Families of Generators 155
The Linear Evolution Equation 165
Examples of Linear Evolution Equations 177
Scalar Fields in the Gravitational Field of a Spherical Black Hole 178
Non-Autonomous Linear Hermitian Hyperbolic Systems 199
The Quasi-Linear Evolution Equation 215
Examples of Quasi-Linear Evolution Equations 235
A Generalized Inviscid Burgers' Equation 235
Quasi-Linear Hermitian Hyperbolic Systems 246
Appendix 265
References 269
Index of Notation 279
Index of Terminology 281
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Petra Hartmann
reviewed Beyond Partial Differential Equations: On Linear and Quasi-Linear Abstract Hyperbolic Evolution Equations on June 15, 2017
Beyond Partial Differential Equations
I really don't understand why this book isn't rated any higher? This prepared me for AP Calc brilliantly and I actually asked my High School if I could buy this textbook from them.
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