Marin M., Öchsner A. Essentials of Partial Differential Equations: With Applications

Springer, 2019. — 383 p. — ISBN: 3319906461.This book was written based on lectures and tutorials held for mathematics and computer science students. Supplementary notions were added to these notes in order to make the reader refer to the bibliography as little as possible. The present form of the book is due to the essential contributions of our published results. We divided the book into two parts, thus suggesting that the path of the student in mathematics (and other subjects), starting with an introduction into the theory of partial differential equations and then leading into the modern problems of this subject, can be done in two steps.Classical Solutions
Quasilinear Equations
Differential Operators of Second Order
The Theory of Potential
Boundary Value Problems for Elliptic Operators
Operational Calculus
Parabolic Equations
Hyperbolic Equations
Solutions in Distributions
Elements of Distributions
Integral Formulas
Partial Differential Equations of the First Order
Linear Partial Differential Equations of Second Order
Harmonic Functions
Weak Solutions of Classical Problems
Regularity of the Solutions
Weak Solutions for Parabolic Equations
Weak Solutions for Hyperbolic Equations