Initial-Boundary Value Problems for Nonlinear Parabolic Equations in Higher Dimensional Domains 下载 pdf 2025 网盘 epub 在线 mobi 免费

This book deal with nonlinear parboic epuations and systems of second order in higher dimensional domains, aninly several initial-boundary value problems for nonlinear parabolic equations and systems of second order equatiohns with smooth coefficents or measurable coefficients are dixcussed. There are two characteristics of this booku. One is that parabolic equations are discussed in the nonilinear case and the boundary condittions include the irregualr oblique derivative case, another one is that boundary value problems are almost consicered in the case of multiply connected domains and several methotds anr used. This booku can be refered to the graduate students, researchers in partial differential equations and function theory at universites and institutes.

Preface

Chapter Ⅰ Properties of Solutions for Parabolic Equations of Second Order

1. Conditions of Linear and Nonlinear Parabolic Equations of Second Ordes

2. Exteremum Principles of Soutions for Parabolic Parabolic Equations Second Order

3. Uniqueness and Stability of Soutions for Parabolic Parabolic Equations Second Order

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

5. Aleksandrov-Bakel man-Pucci Type Maximum Principle

ChapterⅡ Nonlinear Parabolic Equations of Second Order With Smooth Coefficients

1. Formulation of Initial-Irregular Oblique Derivative Problem for Nonlinear Parablic Equations with Smooth Coefficients

2. Boundedness and Holder Estimates of Soolutions of InitialRegular Oblique Derivative Prblem for Eqauation(1.2)

3. Boundeness and Holder Estimates of Derivatives of Solutions of Initial-Regular Oblique Derivative Problem for Equation(1.2)

4. A Priori Estimates of Derivatives of Solutions of Intial-Irregular Oblique Derivative Problem for Equation(1.2)

5. Solvability of the Initial-Irregular Oblique Derivative Problem for Equation(1.2)

ChapterⅢ Nonlinear Parabolic Equations of Second Order With Cordes )(Measurable)Coefficients

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

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

3. The Dirichlet Problem and Nuemann Problem for Nonlinear Parabolic Equations

4. Initial-Oblique Derivative Problem for Nonlinear Parabolic Equations

5. Initial-Mixed Boundary Value Problems for Nonlinear Parabolic Equations

ChapterⅥ Nonlinear Parabolic Systems of Equations Withe Cordes(Measurable)Coefficients

……

ChapterⅤ Linear and Quasilinear Parabolic Equations with VMO(measurable)Coefficients

References

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《非线形抛物线方程在高维区域中的初:边值问题(英文版)》：This book deals with nonlinear parabolic equations and systems of second order in higher dimensional domains, mainly several initial-boundary value problems for nonlinear parabolic equations and systems of second order equations with smooth coefficients or measuxrable coefficients are discussed. There are two characteristics of this book. One is that parabolic equations are discussed in the nonlinear case and the boundary conditions include the irregular oblique derivative case, another one is that boundary value problems are almost considered in the case of multiply connected domains and several methods are used. This book can be refered to the graduate students, reseachers in partial differential equations and function theory at universities and institutes.