XII. The Initial Value Problem for Nonlinear Hyperbolic Equations in Two Independent Variables

Kapitel in diesem Buch

1. Frontmatter i
2. Foreword v
3. Contents vii
4. I. Green’s Formula and Analytic Continuation 1
5. II. Strongly Elliptic Systems of Differential Equations 15
6. III. Derivatives of Solutions of Linear Elliptic Partial Differential Equations 53
7. IV. On Multivalued Solutions of Linear Partial Differential Equations 63
8. V. Function-Theoretical Properties of Solutions of Partial Differential Equations of Elliptic Type 69
9. VI. On a Generalization of Quasi-Conformal Mappings and its Application to Elliptic Partial Differential Equations 95
10. VII. Second Order Elliptic Systems of Differential Equations 101
11. VIII. Conservation Laws of Certain Systems of Partial Differential Equations and Associated Mappings 161
12. IX. Parabolic Equations 167
13. X. Linear Equations of Parabolic Type with Constant Coefficients 191
14. XI. On Linear Hyperbolic Differential Equations with Variable Coefficients on a Vector Space 201
15. XII. The Initial Value Problem for Nonlinear Hyperbolic Equations in Two Independent Variables 211
16. XIII. A Geometric Treatment of Linear Hyperbolic Equations of Second Order 231
17. XIV. On Cauchy’s Problem and Fundamental Solutions 235
18. XV. A Boundary Value Problem for the Wave Equation and Mean Value Theorems 249
19. Backmatter 259