1.

Record Nr.

UNINA9910634038403321

Autore

Salsa S.

Titolo

Partial Differential Equations in Action : From Modelling to Theory / / by Sandro Salsa, Gianmaria Verzini

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022

ISBN

3-031-21853-1

Edizione

[4th ed. 2022.]

Descrizione fisica

1 online resource (692 pages)

Collana

La Matematica per il 3+2, , 2038-5757 ; ; 147

Disciplina

381

515.353

Soggetti

Differential equations

Engineering mathematics

Engineering - Data processing

Functional analysis

Mathematical physics

Differential Equations

Mathematical and Computational Engineering Applications

Functional Analysis

Mathematical Methods in Physics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

1 Introduction -- 2 Diffusion -- 3 The Laplace Equation -- 4 Scalar Conservation Laws and First Order Equations -- 5 Waves and Vibration -- 6 Elements of Functional Analysis -- 7 Distributions and Sobolev Spaces -- 8 Variational Formulation of Elliptic Problems -- 9 Weak Formulation of Evolution Problems -- 10 More Advanced Topics -- 11 Systems of Conservation Laws -- Appendix A: Measures and Integrals -- Appendix B: Identities and Formulas.

Sommario/riassunto

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.