Linear and Quasilinear Complex Equations of Hyperbolic and Mixed Types

by Chun Wen; Guo

• ISBN13: 9780415269711
• ISBN10: 0415269717
• Format: Hardcover
• Copyright: 2002-08-22
• Publisher: CRC Press

Summary

This volume deals with first and second order complex equations of hyperbolic and mixed types. Various general boundary value problems for linear and quasilinear complex equations are investigated in detail. To obtain results for complex equations of mixed types, some discontinuous boundary value problems for elliptic complex equations are discussed. Mixed complex equations are included in the quasilinear case, and the text considers both boundary value conditions in the general oblique derivative case and multiply connected domains. Complex analytical methods are used to investigate various problems as well. In particular, hyperbolic numbers and hyperbolic complex functions are introduced to handle hyperbolic complex equations. Researchers and graduate students in mathematical analysis will find this text indispensable.

Author Biography

Guo Chun Wen is Professor in the School of Mathematical Sciences, Peking University, Beijing.

Table of Contents

Introduction to the series	p. viii
Preface	p. ix
Hyperbolic complex equations of first order	p. 1
Hyperbolic complex functions and hyperbolic pseudoregular functions	p. 1
Complex forms of linear and nonlinear hyperbolic systems of first order equations	p. 10
Boundary value problems of linear hyperbolic complex equations of first order	p. 18
Boundary value problems of quasilinear hyperbolic complex equations of first order	p. 25
Hyperbolic mappings and quasi-hyperbolic mappings	p. 35
Hyperbolic complex equations of second order	p. 39
Complex form of hyperbolic equations of second order	p. 39
Oblique derivative problems for quasilinear hyperbolic equations of second order	p. 43
Oblique derivative problems for general quasilinear hyperbolic equations of second order	p. 50
Other oblique derivative problems for quasilinear hyperbolic equations of second order	p. 59
Oblique derivative problems for degenerate hyperbolic equations of second order	p. 66
Nonlinear elliptic complex equations of first and second order	p. 79
Generalizations of Keldych--Sedov formula for analytic functions	p. 79
Representation and existence of solutions for elliptic complex equations of first order	p. 90
Discontinuous oblique derivative problems for quasilinear elliptic equations of second order	p. 95
Boundary value problems for degenerate elliptic equations of second order in a simply connected domain	p. 108
First order complex equations of mixed type	p. 119
The Riemann--Hilbert problem for simplest first order complex equation of mixed type	p. 119
The Riemann--Hilbert problem for first order linear complex equations of mixed type	p. 126
The Riemann--Hilbert problem for first order quasilinear complex equations of mixed type	p. 134
The Riemann--Hilbert problem for first order quasilinear quations of mixed type in general domains	p. 138
The discontinuous Riemann--Hilbert problem for quasilinear mixed equations of first order	p. 143
Second order linear equations of mixed type	p. 157
Oblique derivative problems for simplest second order equation of mixed type	p. 157
Oblique derivative problems for second order linear equations of mixed type	p. 162
Discontinuous oblique derivative problems for second order linear equations of mixed type	p. 171
The Frankl boundary value problem for second order linear equations of mixed type	p. 177
Oblique derivative problems for second order degenerate equations of mixed type	p. 194
Second order quasilinear equations of mixed type	p. 200
Oblique derivative problems for second order quasilinear equations of mixed type	p. 200
Oblique derivative problems for second order equations of mixed type in general domains	p. 209
Discontinuous oblique derivative problems for second order quasilinear equations of mixed type	p. 218
Oblique derivative problems for quasilinear equations of mixed type in multiply connected domains	p. 227
References	p. 240
Index	p. 250
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