Partial Dynamic Equations
Wave, Parabolic and Elliptic Equations on Time Scales
- English
- ePUB (mobile friendly)
- Available on iOS & Android
About this book
This book is devoted to the qualitative theory of partial dynamic equations on arbitrary time scales. The results in the book generalize the classical results, and they unify the discrete and continuous cases. The book starts with classification and canonical forms for second-order PDEs. Next, the Laplace transform method and the Fourier transform method are introduced. The Fourier transform is applied to solving second-order PDEs. The method of separation of variables is considered later in the book. The following few chapters are devoted to factoring second-order PDEs, including the wave equation, the heat equation, and the Laplace equation. It proves the weak maximum principle and as its application is investigated the stability of the solutions of the Poisson equation. Finally, the reduction of some nonlinear PDEs to the wave equation, the heat equation, and the Laplace equation are discussed. ?he main advantage of the book is that it offers a variety of analytical techniques for the study of partial dynamical equations and that the results obtained over arbitrary time scales can be used to derive results in the classical case and in the discrete case.
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Information
Table of contents
- Title Page
- Copyright
- Contents
- 1âClassification of second-order partial dynamic equations
- 2âClassification and canonical forms for linear second-order partial dynamic equations in two independent variables
- 3âThe Laplace transform method
- 4âThe Fourier transform method
- 5âMethod of separation of variables
- 6âMethod of factoring
- 7âThe wave equation
- 8âThe heat equation
- 9âThe Laplace equation
- 10âReduction of some partial dynamic equations
- Subject Index