This volume contains the proceedings of a NATO/London Mathematical
Society Advanced Study Institute held in Oxford from 25 July - 7 August
1982. The institute concerned the theory and applications of systems of
nonlinear partial differential equations, with emphasis on techniques
appropriate to systems of more than one equation. Most of the lecturers
and participants were analysts specializing in partial differential
equations, but also present were a number of numerical analysts, workers
in mechanics, and other applied mathematicians. The organizing committee
for the institute was J.M. Ball (Heriot-Watt), T.B. Benjamin (Oxford),
J. Carr (Heriot-Watt), C.M. Dafermos (Brown), S. Hildebrandt (Bonn) and
J.S. pym (Sheffield) . The programme of the institute consisted of a
number of courses of expository lectures, together with special sessions
on different topics. It is a pleasure to thank all the lecturers for the
care they took in the preparation of their talks, and S.S. Antman, A.J.
Chorin, J.K. Hale and J.E. Marsden for the organization of their special
sessions. The institute was made possible by financial support from
NATO, the London Mathematical Society, the u.S. Army Research Office,
the u.S. Army European Research Office, and the u.S. National Science
Foundation. The lectures were held in the Mathematical Institute of the
University of Oxford, and residential accommodation was provided at
Hertford College.