Weak Solutions of Partial Differential Equations
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Beschreibung
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.
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.
Covers elliptic, parabolic, and hyperbolic PDE Presents compactness results for parabolic problems in detail Includes a detailed study of the Riemann problem for systems of nonlinear hyperbolic equations
Autor*in
Thierry Gallouët
Themen in »Weak Solutions of Partial Differential Equations«
elliptic partial differential equations parabolic partial differential equations nonlinear PDE existence and uniqueness of solutions of PDE Sobolev spaces Schauder fixed point topological degree compactness methods for PDE heat equation Leray-Lions problem Stefan problem Aubin-Simon theorem entropy solutions Riemann problem Saint-Venant equation