Problems on Partial Differential Equations

ISBN-13: 9783030147334 / Angielski / Twarda / 2019 / 248 str.

Maciej Borodzik; Pawel Goldstein; Piotr Rybka

Recenzje

"This book can be helpful in the preparation of a PDE course providing a choice of exercises, but also it can be used by students to get an independent introduction to PDE theory and to deepen their understanding of solving the collected problems." (Sergey Dashkovskiy, Mathematical Reviews, March 2, 2020)
"This book represents an important tool in the study of PDEs for the students as well for the teachers by adopting 'a perspective on PDEs that is neither too theoretical nor too practical' representing 'the perfect companion to a broad spectrum of courses'." (Cristian Chifu, zbMATH 1421.35001, 2019)

Spis treści

Preliminaries.- Distributions, Sobolev spaces and Fourier transform.- Common methods.- Elliptic equations.- Evolution equations.- Bibliography.

O autorze

Maciej Borodzik, the University of Warsaw, Warsaw, Poland

Paweł Goldstein, the University of Warsaw, Warsaw, Poland

Piotr Rybka, the University of Warsaw, Warsaw, Poland

Anna Zatorska-Goldstein, the University of Warsaw, Warsaw, Poland

Blurb

This book covers a diverse range of topics in Mathematical Physics, linear and nonlinear PDEs. Though the text reflects the classical theory, the main emphasis is on introducing readers to the latest developments based on the notions of weak solutions and Sobolev spaces.

In numerous problems, the student is asked to prove a given statement, e.g. to show the existence of a solution to a certain PDE. Usually there is no closed-formula answer available, which is why there is no answer section, although helpful hints are often provided.

 

This textbook offers a valuable asset for students and educators alike. As it adopts a perspective on PDEs that is neither too theoretical nor too practical, it represents the perfect companion to a broad spectrum of courses.