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Book review

Author(s) Antman, S.S. (ed.)
Ericksen, J.L. (ed.)
Kinderlehrer, D. (ed.)
Müller, I. (ed.)
Title Metastability and Incompletely Posed Problems
Publisher Springer-Verlag
Year of publication 1987
Reviewed by Yurii Rybakov, Valery Sanyuk

The reviewed volume represents the proceedings of the workshop held under the IMA (Institute for Mathematics & Applications) 1984-1985 program on continuum physics and partial differential equations. The contributed papers may be devided into two parts. The first part involves the wide spectrum of applied results in concern with the dissipative mechanisms in nonlinear viscoelastic media, bifurcation problems in constrained nonlinear thermoelasticity, the problems in crystal elasticity, and nonlocal problems in electromagnetism, including the generalization of the Ohm's law and nonlocal constitutive model for ferromagnetic matherials.

The other papers of the volume discuss purely mathematical problems of the calculus of variations, such as quasiconvexity and partial regularity of minimizers, stability of nonlinear waves and existence of metastable harmonic maps. These listed problems became rather popular in modern physical applications (chiral models in nuclear and partical physics, theory of nematic liquid crystals, theory of magnetic exitations and so on).

Thus, it is possible to say that the volume represents two rather distinct levels in the investigation of the problems posed in its title, therewith it stands out in the current literature on the subject. Thou the price is high enough for this camera-ready book (with a slight excuse that it has been prepared for publication before the TeX epoch), there is no doubt that it will find its reader. First of all the mathematical methods elaborated in the papers might be of great interest for those physicits from different fields, who are looking for rigorous results. Next large market might consists of specialists in applied or engineering science, who will find in the book a plenty of encouraging results and advanced good-working methods to study otherwise unapproachable problems. It might be a sound investment as well for specialists from other branches of fundamental and applied science.