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# Partial Differential Equations in Action: From Modelling to Theory

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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.

Συγγραφείς: Salsa Sandro, Verzini Gianmaria
Εκδότης: SPRINGER
Σελίδες: 677
ISBN: 9783031218521
Εξώφυλλο: Μαλακό Εξώφυλλο
Αριθμός Έκδοσης: 4
Έτος έκδοσης: 2022

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.

Sandro Salsa is a Professor of Mathematical Analysis at the Department of Mathematics of the 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 free boundary problems. He is an author of 13 books and several papers in the most prestigious scientific mathematical journals.

Gianmaria Verzini, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy.