Linear and nonlinear parabolic complex equations / Guo Chun Wen.

Format:

Book

Author/Creator:

Wen, Guo Chun.

Language:

English

Subjects (All):

Differential equations, Parabolic.

Functions of complex variables.

Physical Description:

ix, 246 pages ; 23 cm

Place of Publication:

Singapore ; River Edge, N.J. : World Scientific, [1999]

Summary:

This book deals mainly with linear and nonlinear parabolic equations and systems of second and fourth order. It first transforms the real forms of parabolic equations and systems into complex forms, and then discusses several initial boundary value problems and Cauchy problems for quasilinear and nonlinear parabolic complex equations of second order with smooth coefficients or measurable coefficients. Parabolic complex equations are discussed in the nonlinear case and the boundary conditions usually include the initial irregular oblique derivative. The boundary value problems are considered in multiply connected domains and several methods are used.

Contents:

I Properties of Solutions for Parabolic Complex Equations of Second Order 1

1. Complex Forms of Linear and Nonlinear Parabolic Equations of Second Order 1

2. Extremum Principles of Solutions for Parabolic Complex Equations of Second Order 5

3. Uniqueness and Stability of Solutions for Some Initial-Boundary Value Problems for Parabolic Equations 12

4. Representation Theorem and Compactness Theorem of Solutions for Parabolic Equations 19

II Quasilinear Parabolic Complex Equations of Second Order with Smooth Coefficients 31

1. Conditions of Quasilinear Parabolic Equations of Second Order 31

2. A Priori Estimates of Solutions of Dirichlet Boundary Value Problem for Complex Equations of Second Order 36

3. Existence of Solutions of Dirichlet Boundary Value Problem for Complex Equations of Second Order 51

4. Initial-Regular Oblique Derivative Problem for Complex Equations of Second Order 53

III Nonlinear Parabolic Complex Equations of Second Order with Smooth Coefficients 63

1. Conditions of Nonlinear Parabolic Complex Equations of Second Order with Smooth Coefficients 63

2. A Priori Estimates of Solutions for the Dirichlet Boundary Value Problem 67

3. Solvability of Dirichlet Boundary Value Problem for Complex Equations of Second Order 87

4. Initial-Regular Oblique Derivative Problem for Complex Equations of Second Order 90

5. Initial-Irregular Oblique Derivative Problem for Complex Equations 102

IV Nonlinear Parabolic Complex Equations of Second Order with Measurable Coefficients 113

1. Formulation of Initial-Boundary Value Problems for Nonlinear Parabolic Equations 113

2. Inner Estimates of Solutions for Initial-Boundary Value Problems 116

3. A Priori Estimates of Solutions and Solvability of the Dirichlet Boundary Value Problem 126

4. A Priori Estimates of Solutions and Solvability of the Initial-Regular Oblique Derivative Problem 134

5. Initial-Mixed Boundary Value Problem for Parabolic Complex Equations of Second Order 140

6. Initial-Irregular Oblique Derivative Problems for Parabolic Equations of Second Order 145

V Nonlinear Parabolic Complex Systems of Second Order Equations with Measurable Coefficients 157

1. Formulation and Uniqueness of Initial-General Boundary Value Problems for Nonlinear Parabolic Systems 157

2. The First Boundary Value Problem for Parabolic Systems of Second Order Equations 163

3. Initial-Regular Oblique Derivative Problems for Parabolic Systems of Second Order Equations 171

4. Initial-Irregular Oblique Derivative Problems for Parabolic Systems of Second Order Equations 179

5. Initial-Mixed Boundary Value Problems for Parabolic Systems of Second Order Equations 190

VI Cauchy Problems for Nonlinear Parabolic Equations and Systems of Second Order 199

1. Cauchy Problem for Nonlinear Parabolic Equations of Second Order with Measurable Coefficients 199

2. Cauchy Problem for Nonlinear Parabolic Systems of Second Order Equations with Measurable Coefficients 205

3. Cauchy Problem for Quasilinear Parabolic Equations of Second Order with Smooth Coefficients 211

4. Cauchy Problem for Quasilinear Parabolic Systems of Second Order Equations with Smooth Coefficients 220.

Notes:

Includes bibliographical references (pages 229-239) and index.

ISBN:

9810238568

OCLC:

40744370