Ebook: Nonlinear Partial Differential Equations: Asymptotic Behavior of Solutions and Self-Similar Solutions
- Tags: Partial Differential Equations, Functional Analysis, Analysis, Approximations and Expansions
- Series: Progress in Nonlinear Differential Equations and Their Applications 79
- Year: 2010
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
The main focus of this textbook, in two parts, is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. The exposition moves systematically from the basic to more sophisticated concepts with recent developments and several open problems. With challenging exercises, examples, and illustrations to help explain the rigorous analytic basis for the Navier–-Stokes equations, mean curvature flow equations, and other important equations describing real phenomena, this book is written for graduate students and researchers, not only in mathematics but also in other disciplines.
Nonlinear Partial Differential Equations will serve as an excellent textbook for a first course in modern analysis or as a useful self-study guide. Key topics in nonlinear partial differential equations as well as several fundamental tools and methods are presented. The only prerequisite required is a basic course in calculus.
The main focus of this textbook, in two parts, is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. The exposition moves systematically from the basic to more sophisticated concepts with recent developments and several open problems. With challenging exercises, examples, and illustrations to help explain the rigorous analytic basis for the Navier–-Stokes equations, mean curvature flow equations, and other important equations describing real phenomena, this book is written for graduate students and researchers, not only in mathematics but also in other disciplines.
Nonlinear Partial Differential Equations will serve as an excellent textbook for a first course in modern analysis or as a useful self-study guide. Key topics in nonlinear partial differential equations as well as several fundamental tools and methods are presented. The only prerequisite required is a basic course in calculus.
The main focus of this textbook, in two parts, is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. The exposition moves systematically from the basic to more sophisticated concepts with recent developments and several open problems. With challenging exercises, examples, and illustrations to help explain the rigorous analytic basis for the Navier–-Stokes equations, mean curvature flow equations, and other important equations describing real phenomena, this book is written for graduate students and researchers, not only in mathematics but also in other disciplines.
Nonlinear Partial Differential Equations will serve as an excellent textbook for a first course in modern analysis or as a useful self-study guide. Key topics in nonlinear partial differential equations as well as several fundamental tools and methods are presented. The only prerequisite required is a basic course in calculus.
Content:
Front Matter....Pages i-xviii
Front Matter....Pages 1-1
Behavior Near Time Infinity of Solutions of the Heat Equation....Pages 3-36
Behavior Near Time Infinity of Solutions of the Vorticity Equations....Pages 37-103
Self-Similar Solutions for Various Equations....Pages 105-138
Front Matter....Pages 140-140
Various Properties of Solutions of the Heat Equation....Pages 141-180
Compactness Theorems....Pages 181-188
Calculus Inequalities....Pages 189-238
Convergence Theorems in the Theory of Integration....Pages 239-247
Back Matter....Pages 249-294
The main focus of this textbook, in two parts, is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. The exposition moves systematically from the basic to more sophisticated concepts with recent developments and several open problems. With challenging exercises, examples, and illustrations to help explain the rigorous analytic basis for the Navier–-Stokes equations, mean curvature flow equations, and other important equations describing real phenomena, this book is written for graduate students and researchers, not only in mathematics but also in other disciplines.
Nonlinear Partial Differential Equations will serve as an excellent textbook for a first course in modern analysis or as a useful self-study guide. Key topics in nonlinear partial differential equations as well as several fundamental tools and methods are presented. The only prerequisite required is a basic course in calculus.
Content:
Front Matter....Pages i-xviii
Front Matter....Pages 1-1
Behavior Near Time Infinity of Solutions of the Heat Equation....Pages 3-36
Behavior Near Time Infinity of Solutions of the Vorticity Equations....Pages 37-103
Self-Similar Solutions for Various Equations....Pages 105-138
Front Matter....Pages 140-140
Various Properties of Solutions of the Heat Equation....Pages 141-180
Compactness Theorems....Pages 181-188
Calculus Inequalities....Pages 189-238
Convergence Theorems in the Theory of Integration....Pages 239-247
Back Matter....Pages 249-294
....