Georgiev S. Multiplicative Partial Differential Equations 2023

Textbook in PDF format

This book presents an introduction to the theory of multiplicative partial differential equations (MPDEs). It is suitable for all types of basic courses on MPDEs. The author’s aim is to present a clear and well-organized treatment of the concept behind the development of mathematics and solution techniques. The text material of this book is presented in highly readable, mathematically solid format. Many practical problems are illustrated displaying a wide variety of solution techniques.
The book features:
The book includes new classification and canonical forms of Second order MPDEs.
Proposes a new technique to solve the multiplicative wave equation such as method of separation of variables, energy method.
The proposed technique in the book can be used to give 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, theorems of Liouville and Harnack