Multiplication of Distributions: A Tool in Mathematics, Numerical Engineering and Theoretical Physics

ISBN-13: 9783540562887 / Angielski / Miękka / 1992 / 186 str.

Jean F. Colombeau

Opis

This book presents recent and very elementary developmentsof a theory of multiplication of distributions in the fieldof explicit and numerical solutions of systems of PDEs ofphysics (nonlinear elasticity, elastoplasticity, hydrodynamics, multifluid flows, acoustics). Theprerequisites are kept to introductory calculus level sothat the book remains accessible at the same time to puremathematicians (as a smoothand somewhat heuristicintrodcution to this theory) and to applied mathematicians, numerical engineers and theoretical physicists (as a tool totreat problems involving products of distributions).

Spis treści

to generalized functions and distributions.- Multiplications of distributions in classical physics.- Elementary introduction.- Jump formulas for systems in nonconservative form. New numerical methods.- The case of several constitutive equations.- Linear wave propagation in a medium with piecewise C? characteristics.- The canonical Hamiltonian formalism of interacting quantum fields.- The abstract theory of generalized functions.