Partial Differential EquationsSpringer Science & Business Media, 20 nov. 1991 - 252 pages This book is a very well-accepted introduction to the subject. In it, the author identifies the significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy’s example of a linear equation without solutions. |
Table des matières
Chapter | 1 |
Quasilinear Equations | 9 |
Chapter 3 | 39 |
Chapter 8 | 53 |
Characteristic Manifolds and the Cauchy Problem | 54 |
The Cauchy Problem | 58 |
The LagrangeGreen Identity | 79 |
Distribution Solutions | 89 |
45 | 137 |
HigherOrder Hyperbolic Equations with Constant Coefficients | 143 |
www | 150 |
Symmetric Hyperbolic Systems | 163 |
37 | 175 |
Chapter 6 | 185 |
More on the Hilbert Space H and the Assumption of Boundary Values | 198 |
Chapter 7 | 206 |
The Maximum Principle | 103 |
Proof of Existence of Solutions for the Dirichlet Problem Using | 111 |
Solution of the Dirichlet Problem by HilbertSpace Methods | 117 |
Chapter 5 | 126 |
The OneDimensional Wave Equation | 128 |
The InitialValue Problem for General SecondOrder Linear | 227 |
H Lewys Example of a Linear Equation | 235 |
Bibliography | 241 |
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Expressions et termes fréquents
assume ball belongs bounded Cauchy data Cauchy problem Cauchy sequence Chapter characteristic curves class C² coefficients compact subset compact support complex cone constant continuous converge defined denote derivatives of orders determined uniquely Dirichlet problem domain of dependence elliptic exists follows formula Fourier function f fundamental solution given harmonic function hence Hilbert space Hint holds identity implies inequality initial conditions initial data initial values initial-value problem integral surface Laplace equation Lemma linear matrix maximum principle neighborhood non-characteristic obtained open set ordinary differential equations partial differential equation plane polynomial power series prescribed proof quasi-linear real analytic functions real numbers satisfies scalar second derivatives Show solved sufficiently small test function u₁ uniformly vanish vector wave equation x₁ ΘΩ ди