Multiplication of Distributions: A tool in mathematics, numerical engineering and theoretical physics

Jean François Colombeau (auth.)3540562885, 9783540562887, 0387562885

This book presents recent and very elementary developments of a theory of multiplication of distributions in the field of explicit and numerical solutions of systems of PDEs of physics (nonlinear elasticity, elastoplasticity, hydrodynamics, multifluid flows, acoustics). The prerequisites are kept to introductory calculus level so that the book remains accessible at the same time to pure mathematicians (as a smoothand somewhat heuristic introdcution to this theory) and to applied mathematicians, numerical engineers and theoretical physicists (as a tool to treat problems involving products of distributions).

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Table of contents :
Introduction to generalized functions and distributions….Pages 1-12
Multiplications of distributions in classical physics….Pages 13-29
Elementary introduction….Pages 30-61
Jump formulas for systems in nonconservative form. New numerical methods….Pages 62-96
The case of several constitutive equations….Pages 97-123
Linear wave propagation in a medium with piecewise C ∞ characteristics….Pages 124-143
The canonical Hamiltonian formalism of interacting quantum fields….Pages 144-157
The abstract theory of generalized functions….Pages 158-171