1st Edition
Multiplicative Partial Differential Equations
Multiplicative Partial Differential Equations presents an introduction to the theory of multiplicative partial differential equations (MPDEs). It is suitable for all types of basic courses on MPDEs. The authors' aim is to present a clear and well-organized treatment of the concepts behind the development of mathematics and solution techniques. The text is presented in a highly readable, mathematically solid format. Many practical problems are illustrated, displaying a wide variety of solution techniques.
Features
- Includes new classification and canonical forms of second-order MPDEs
- Proposes the latest techniques in solving the multiplicative wave equation such as the method of separation of variables and the energy method
- Useful in allowing for the basic properties of multiplicative elliptic problems, fundamental solutions, multiplicative integral representation of multiplicative harmonic functions, meant-value formulas, strong principle of maximum, multiplicative Poisson equation, multiplicative Green functions, method of separation of variables, and theorems of Liouville and Harnack
1. 1. General Introduction
2. 2. Classification of Second Order Multiplicative Partial Differential Equations
3. 3. Classification and Canonical Forms
4. 4. The Multiplicative Wave Equation
5. 5. The Heat Equation
6. 6. The Laplace Equation
7. 7. The Cauchy-Kovalevskaya Theorem
Biography
Svetlin G. Georgiev has worked in various areas of mathematics. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations and dynamic calculus on time scales.
Khaled Zennir received his PhD in mathematics in 2013 from Sidi Bel Abbès University, Algeria (assist. professor). He obtained his highest diploma in Algeria (habilitation, mathematics) from Constantine University, Algeria in 2015 (assoc. professor). He is now an associate professor at Qassim University, KSA. His research interests lie in nonlinear hyperbolic partial differential equations: global existence, blow-up and long time behavior.
