Offers an exposition on free boundary problems. Free or moving boundary problems appear in many areas of analysis, geometry, and applied mathematics. This book is useful for supplementary reading or as an independent study text. It is also suitable for gra

Il testo e rivolto a studenti di Ingegneria, Matematica Applicata e Fisica ed e disegnato per corsi alle fine del triennio o all'inizio del biennio magistrale. obiettivo didattico e duplice: da un lato presentare ed analizzare alcuni classici modelli differenziali della Meccanica dei Continui, completati da esercizi svolti e da simulazioni numeriche, illustrate usando il metodo delle differenze finite; dall'altro introdurre la formulazione variazionale dei piu importanti problemi iniziali/al bordo, accompagnate da simulazioni numeriche effettuate utilizzando il metodo degli elementi finiti....

La presente raccolta di problemi ed esercizi nasce dall'esperienza maturata durante il corso di Equazioni a Derivate Parziali (EDPed e rivolto prevalentemente a studenti di Ingegneria, Fisica e Matematica, ma costituisce un utile punto di riferimento anche per coloro che desiderano approfondire alcuni aspetti teorici e modellistici di questa importante disciplina. La finalita consiste nell'abituare il lettore ad una sinergia metodologica nell'affrontare problemi teorici e/o modellistici.

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This book offers students a solid introduction to numerical methods, such as finite differences and finite elements. Each chapter ends with a brief introduction to numerical approximation techniques for the specific problem at hand.

This textbook presents problems and exercises at various levels of difficulty in the following areas: Classical Methods in PDEs (diffusion, waves, transport, potential equations); Basic Functional Analysis and Distribution Theory; Variational Formulation of Elliptic Problems; and Weak Formulation for Parabolic Problems and for the Wave Equation. Thanks to the broad variety of exercises with complete solutions, it can be used in all basic and advanced PDE courses.

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...

This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance.The first introductory chapter...