Distribution Theory Applied to Differential Equations
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Beschreibung
This book presents important contributions to modern theories concerning the distribution theory applied to convex analysis (convex functions, functions of lower semicontinuity, the subdifferential of a convex function). The authors prove several basic results in distribution theory and present ordinary differential equations and partial differential equations by providing generalized solutions. In addition, the book deals with Sobolev spaces, which presents aspects related to variation problems, such as the Stokes system, the elasticity system and the plate equation. The authors also include approximate formulations of variation problems, such as the Galerkin method or the finite element method.
The book is accessible to all scientists, and it is especially useful for those who use mathematics to solve engineering and physics problems. The authors have avoided concepts and results contained in other books in order to keep the book comprehensive. Furthermore, they do not present concrete simplified models and pay maximal attention to scientific rigor.
This book presents important contributions to modern theories concerning the distribution theory applied to convex analysis (convex functions, functions of lower semicontinuity, the subdifferential of a convex function). The authors prove several basic results in distribution theory and present ordinary differential equations and partial differential equations by providing generalized solutions. In addition, the book deals with Sobolev spaces, which presents aspects related to variation problems, such as the Stokes system, the elasticity system and the plate equation. The authors also include approximate formulations of variation problems, such as the Galerkin method or the finite element method.
The book is accessible to all scientists, and it is especially useful for those who use mathematics to solve engineering and physics problems. The authors have avoided concepts and results contained in other books in order to keep the book comprehensive. Furthermore, they do not present concrete simplified models and pay maximal attention to scientific rigor.
Presents important contributions to modern theories concerning the distribution theory applied to convex analysis Includes approximate formulations of variation problems, such as the Galerkin method or the finite element method Is useful for those who use mathematics to solve engineering and physics problems
Autor*in
Adina Chirilă
Themen in »Distribution Theory Applied to Differential Equations«
Sobolev Space Variational Formulation Tempered Distributions Subdifferential Evolution Equations Differential Operators Convex Functions Weak Solutions Finite Element Method Lower-semicontinuous Functions
Stimmen zu »Distribution Theory Applied to Differential Equations«
“This book presents the theory of distributions of Laurent Schwartz and some of its applications to differential equations. … This book seems to be meant for readers who use mathematics to solve engineering and physics problems, and might be useful for them.” (José Bonet, Mathematical Reviews, June, 2023)
“In the present book, the authors give an excellent explanation of the concept of distributions and why this concept is useful in applied mathematics, generally having in mind applications to differential equations. The book is well and clearly written. … In my opinion this book will be interesting for all readers who prefer the symbiosis between the theory of distributions and its practical application to differential equations.” (Andrey Zahariev, zbMATH 1477.46001, 2022)
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