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Full Description
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).
Contents
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.
