Overview
- The book takes an intriguing mixed approach to partial differential equations, shining a modern light on a classic topic
- Many motivations and examples enlighten the interplay between modelling and theory
- Includes both a modelling approach and mathematical techniques for proving rigorous existence and regularity results
Part of the book series: UNITEXT (UNITEXT, volume 147)
Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)
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About this book
This work is an updated version of a book evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In the second part, chapters 6 to 10 concentrate on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems, while Chapter 11 deals with vector-valued conservation laws, extending the theory developed in Chapter 4. The main differences with respect to the previous editions are: a new section on reaction diffusion models for population dynamics in a heterogeneous environment; several new exercises in almost all chapters; a general restyling and a reordering of the last chapters. The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering.
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Keywords
Table of contents (11 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
About the authors
Sandro Salsa is a Emeritus Professor of Mathematical Analysis at Politecnico of Milan, where he has been one of the main founders of the educational program in Mathematical Engineering. His research interest ranges over diverse aspects of nonlinear, nonlocal, singular or degenerate elliptic and parabolic equations, with particular emphasis on boundary behavior, regularity and free boundary problems. He is an author of 14 books and several papers in the most prestigious scientific mathematical journals.
Gianmaria Verzini is a Professor of Mathematical Analysis at the Department of Mathematics of the Politecnico of Milan. He is author of 5 books and more than 50 papers, published on prominent international journals. His scientific interests concern the applications of Nonlinear Analysis to the existence, multiplicity, qualitative properties and regularity of solutions to nonlinear differential equations and systems.
Bibliographic Information
Book Title: Partial Differential Equations in Action
Book Subtitle: From Modelling to Theory
Authors: Sandro Salsa, Gianmaria Verzini
Series Title: UNITEXT
DOI: https://doi.org/10.1007/978-3-031-21853-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Softcover ISBN: 978-3-031-21852-1Published: 09 December 2022
eBook ISBN: 978-3-031-21853-8Published: 08 December 2022
Series ISSN: 2038-5714
Series E-ISSN: 2532-3318
Edition Number: 4
Number of Pages: XVIII, 677
Number of Illustrations: 1 b/w illustrations
Topics: Analysis, Mathematical and Computational Engineering, Functional Analysis, Mathematical Methods in Physics
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