Weak Solutions of Partial Differential Equations
Springer International Publishing (Verlag)
978-3-031-98981-0 (ISBN)
This book offers a comprehensive introduction to the study of solutions of linear and nonlinear partial differential equations, covering elliptic, parabolic and hyperbolic types. It places particular emphasis on the concept of weak solution, a fundamental framework for addressing well-posed problems in PDE theory. The book examines the existence and uniqueness of solutions for various types of PDEs, along with their key properties. Additionally, many of the methods introduced are also applicable for analyzing the convergence of numerical schemes used to approximate these equations. Based on courses taught by the authors, this book is primarily aimed at graduate students and contains numerous exercises and problems with detailed solutions.
Thierry Gallouët was a professor of mathematics at the University of Chambéry (1985 1993), the École Normale Supérieure de Lyon (1993 1997), and the University of Aix-Marseille (1997 2023). A specialist in functional analysis and partial differential equations, particularly in the L1 theory of elliptic and parabolic equations, he later became interested in the numerical resolution of partial differential equations with applications in petroleum and hydraulic engineering. Along with Robert Eymard, he pioneered a general theory of the finite volume method.
Raphaèle Herbin is a professor of mathematics at the University of Aix-Marseille. She specializes in numerical analysis, particularly in the discretization of partial differential equations. She has contributed to the mathematical analysis of finite volume schemes and their application to various fields, such as electrochemistry and fluid mechanics.
1 Sobolev Spaces.- 2 Linear Elliptic Problems.- 3 Quasi-Linear Elliptic Problems.- 4 Parabolic Problems.- 5 Hyperbolic Problems.
| Erscheinungsdatum | 20.07.2025 |
|---|---|
| Reihe/Serie | Mathématiques et Applications |
| Zusatzinfo | XI, 465 p. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | Aubin-Simon theorem • compactness methods for PDE • Elliptic Partial Differential Equations • Entropy Solutions • existence and uniqueness of solutions of PDE • heat equation • Leray-Lions Problem • nonlinear PDE • Parabolic partial differential equations • Riemann problem • Saint-Venant equation • Schauder fixed point • Sobolev spaces • Stefan problem • Topological degree |
| ISBN-10 | 3-031-98981-3 / 3031989813 |
| ISBN-13 | 978-3-031-98981-0 / 9783031989810 |
| Zustand | Neuware |
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