Distribution Theory Applied to Differential Equations

ISBN-13: 9783030671617 / Angielski / Miękka / 2022 / 286 str.

Adina Chirilă; Marin Marin; Andreas ?chsner

Recenzje

"This book presents the theory of distributions of Laurent Schwartz and some of its applications to differential equations. ... This book seems to be meant for readers who use mathematics to solve engineering and physics problems, and might be useful for them." (José Bonet, Mathematical Reviews, June, 2023)

"In the present book, the authors give an excellent explanation of the concept of distributions and why this concept is useful in applied mathematics, generally having in mind applications to differential equations. The book is well and clearly written. ... In my opinion this book will be interesting for all readers who prefer the symbiosis between the theory of distributions and its practical application to differential equations." (Andrey Zahariev, zbMATH 1477.46001, 2022)

Spis treści

Introduction.- Preliminaries.- Convex and Lower-semicontinuous Functions.- The Subdifferential of a Convex Function.- Evolution Equations.- Distributions.- Tempered Distributions.- Differential Equations in Distributions.- Sobolev Spaces.- Variational Problems.- On Some Spaces of Distributions.- On Some Differential Operators.

O autorze

Adina Chirila is Assistant Professor at the Department of Mathematics and Computer Science at Transilvania University of Brasov. She obtained her Bachelor’s degree and her Ph.D. in Mathematics from the same university. As an international experience, she spent two years in Germany at the Rheinische Friedrich-Wilhelms University of Bonn, from where she graduated with a Master’s degree. She was also a visiting doctoral researcher at the University of Padua in Italy. Her scientific interests lie in differential equations, partial differential equations, equations of evolution and scientific computing with applications in mechanics.

Marin Marin is Professor in Mathematics at the Department of Mathematics and Computer Science at Transilvania University of Brasov, Romania. In 1994, he received his Ph.D. in Mathematics at the University of Bucharest, Faculty of Mathematics. Also from the University of Bucharest, the Faculty of Mathematics, he received in 2013 the title of “Habilitat Professor”.  In 2012, he received the “Spiru Haret” award of the Romanian Academy, and in 2019 the title of “Professor Honoris Causa” of the Ovidius University of Constanta. Professor Marin is an eminent scientist in Applied Mathematics and has contributed various books as well as research papers in many valuable SCI indexed journals. His WOS H-index is 36.

Andreas Öchsner is Full Professor of Lightweight Design and Structural Simulation at Esslingen University of Applied Sciences, Germany. After completing his Dipl.-Ing. degree in Aeronautical Engineering at the University of Stuttgart (1997), he served as a research and teaching assistant at the University of Erlangen-Nuremberg from 1997 to 2003 while pursuing his Doctor of Engineering Sciences (Dr.-Ing.) degree. From 2003 to 2006, he was Assistant Professor at the Department of Mechanical Engineering and Head of the Cellular Metals Group affiliated with the University of Aveiro, Portugal. He spent seven years (2007–2013) as Full Professor at the Department of Applied Mechanics, Technical University of Malaysia, where he was also Head of the Advanced Materials and Structure Lab. From 2014 to 2017, he was Full Professor at the School of Engineering, Griffith University, Australia, and Leader of the Mechanical Engineering Program (Head of Discipline and Program Director).

 

Blurb

This book presents important contributions to modern theories concerning the distribution theory applied to convex analysis (convex functions, functions of lower semicontinuity, the subdifferential of a convex function). The authors prove several basic results in distribution theory and present ordinary differential equations and partial differential equations by providing generalized solutions. In addition, the book deals with Sobolev spaces, which presents aspects related to variation problems, such as the Stokes system, the elasticity system and the plate equation. The authors also include approximate formulations of variation problems, such as the Galerkin method or the finite element method.

The book is accessible to all scientists, and it is especially useful for those who use mathematics to solve engineering and physics problems. The authors have avoided concepts and results contained in other books in order to keep the book comprehensive. Furthermore, they do not present concrete simplified models and pay maximal attention to scientific rigor.