portada Fundamental Solutions of Linear Partial Differential Operators: Theory and Practice (en Inglés)

Fundamental Solutions of Linear Partial Differential Operators: Theory and Practice (en Inglés)

Formato

Libro Físico

Autor

Peter Wagner

Norbert Ortner

Editorial

Springer

Idioma

Inglés

N° páginas

398

Encuadernación

Tapa Blanda

Dimensiones

23.4x15.6x2.1 cm

Peso

0.58 kg.

ISBN13

9783319367996

Categorías

Análisis funcional y transformaciones
Cálculo diferencial y ecuaciones

Fundamental Solutions of Linear Partial Differential Operators: Theory and Practice (en Inglés)

Peter Wagner (Autor) · Norbert Ortner (Autor) · Springer · Tapa Blanda

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Reseña del libro "Fundamental Solutions of Linear Partial Differential Operators: Theory and Practice (en Inglés)"

This monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations. Many illustrative examples also show techniques for finding such solutions in terms of integrals. Particular attention is given to developing the fundamentals of distribution theory, accompanied by calculations of fundamental solutions. The main part of the book deals with existence theorems and uniqueness criteria, the method of parameter integration, the investigation of quasihyperbolic systems by means of Fourier and Laplace transforms, and the representation of fundamental solutions of homogeneous elliptic operators with the help of Abelian integrals. In addition to rigorous distributional derivations and verifications of fundamental solutions, the book also shows how to construct fundamental solutions (matrices) of many physically relevant operators (systems), in elasticity, thermoelasticity, hexagonal/cubic elastodynamics, for Maxwell's system and others. The book mainly addresses researchers and lecturers who work with partial differential equations. However, it also offers a valuable resource for students with a solid background in vector calculus, complex analysis and functional analysis.