Trends in Partial Differential Equations of Mathematical Physics

By J. F. Rodrigues, G. Seregin, and J. M. Urbano (Editors)
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Trends in Partial Differential Equations of Mathematical Physics

J. F. Rodrigues, G. Seregin, and J. M. Urbano (Editors)
Birkhauser (2005) 282 pp., price USD 139.00
ISBN:376437165X
Reviewer: R. Ghrist, University of Illinois, Urbana-Champaign, USA.
Level: advanced.

This volume is a collection of articles from a conference on ``Trends in Partial Differential Equations of Mathematical Physics'' in honor of the 70th birthday of Prof. V. A. Solonnikov from St. Petersburg. Solonnikov's extensive work in elliptic and parabolic PDEs, coercive estimates, free boundary problems, and viscous fluids provides a template for the twenty articles which appear.

The articles are written at a fairly high level, with a four page preface on the life and work of Solonnikov serving as the historical content of the volume. The topics of the articles orbit about viscous fluid dynamics, including non-Newtonian fluids, fluid-fluid interfaces, temparature-driven mass transport in fluids, thermocapillary motion, and Benard convection. A few articles on Eulerian fluids and MHD complement the theme. The remaining articles concern analytical tools and technical estimates.

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