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Textbook:Multiplicative Partial Differential Equations
Author(s): Svetlin G. Georgiev, Khaled Zennir
Sidi Bel Abbès University
Course description:
This course presents an introduction to the theory of multiplicative partial differential equations (MPDEs).
In Chapters 2 and 3, the classification and canonical forms of second-order MPDEs are considered. Chapter 4 is concerned with the multiplicative wave equation. They are investigated by even and odd dimensional multiplicative wave equations, method of separation of variables and energy method. It is introduced as the Riemann functions. Chapter 5 deals with the multiplicative heat equation. They are considered the weak and strong maximum principles, the Cauchy problem, the mean value formula, the method of separation of variables and the energy method. The multiplicative Laplace equation is introduced in Chapter 6. They are given the basic properties of multiplicative elliptic problems, the fundamental solutions, multiplicative integral representation of multiplicative harmonic functions, mean value formulas, strong principle of maximum, the multiplicative Poisson equation, multiplicative Green functions, method of separation of variables and theorems of Liouville and Harnack. Chapter 7 is focused on a multiplicative analogues of the classical Cauchy–Kovalevskaya Theorem. It is considered in the case of both MDEs and MPDEs.
The aim of this course is to present a clear and well-organized treatment of the concept behind the development of mathematics and solution techniques. The text of this coursebook is presented in a highly readable, mathematically solid format. Many practical problems are illustrated displaying a wide variety of solution techniques.
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