E083 Mathematical Theory of Higher-Order Degenerate Evolution Models

Chugunova Marina, Taranets Roman

Kyiv: Akademperiodyka, 2019. — 230 р.

ISBN 978-966-360-382-7

Project «Ukrainian scientific book in a foreign language»

https://doi.org/10.15407/akademperiodyka.382.230

This book is devoted to the study of solvability and qualitative behaviour of generalised solutions to initial boundary value problems for high-order nonlinear parabolic equations and systems. The eventual goal of this book is to present with all rigorous details the new applications of energy-entropy methods starting from one-dimensional problems discussed in Chapters 1-3, progressing to an advanced level in considering these methods for thin-film type systems in Chapter 4, 5 and finally showing all the steps of the qualitative analysis for problems in multi-dimensional domains in Chapter 6. While we expect our readers to be familiar with a parabolic PDE theory and also to have some knowledge of classical functional analysis we do not assume any background in non-linear PDE analysis and provide enough details to learn the methods from the book.