Partial Differential Equations in Action

From Modelling to Theory

Häftad, Engelska, 2022

Av Sandro Salsa, Gianmaria Verzini

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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.

Produktinformation

Utgivningsdatum2022-12-09
Mått155 x 235 x 37 mm
Vikt1 298 g
FormatHäftad
SpråkEngelska
SerieUNITEXT
Antal sidor677
Upplaga4
FörlagSpringer International Publishing AG
ISBN9783031218521

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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.

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.