Bøger i International Series of Numerical Mathematics serien

The Taylor-Couette system is one of the most studied examples of fluid flow exhibiting the spontaneous formation of dynamical structures. In this book, the variety of time independent solutions with periodic spatial structure is numerically investigated by solution of the Navier-Stokes equations.

The application of PDE-based control theory and the corresponding numerical algorithms to industrial problems have become increasingly important in recent years. This volume offers a wide spectrum of aspects of the discipline, and is of interest to mathematicians and scientists working in the field.

The fields of boundary integral equations and of inequality problems, or more gen erally, of nonsmooth mechanics, have seen, in a remarkably short time, a considerable development in mathematics and in theoretical and applied mechanics.

Progress in different fields of mechanics, such as filtra­ tion theory, elastic-plastic problems, crystallization pro­ cesses, internal and surface waves, etc., is governed to a great extent by the advances in the study of free boundary problems for nonlinear partial differential equations. Free boundary problems form a scientific area which attracts attention of many specialists in mathematics and mechanics. Increasing interest in the field has given rise to the "International Conferences on Free Boundary Problems and Their Applications" which have convened, since the 1980s, in such countries as England, the United states, Italy, France and Germany. This book comprises the papers presented at the Interna­ tional Conference "Free Boundary Problems in Continuum Mechanics", organized by the Lavrentyev Institute of Hydrodynamics, Russian Academy of Sciences, July 15-19, 1991, Novosibirsk, Russia. The scientific committee consisted of: Co-chairmen: K.-H. Hoffmann, L.V. Ovsiannikov S. Antontsev (Russia) J. Ockendon (UK) M. Fremond (France) L. Ovsiannikov (Russia) A. Friedman (USA) S. Pokhozhaev (Russia) K.-H. Hoffmann (Germany) M. Primicerio (Italy) A. Khludnev (Russia) V. Pukhnachov (Russia) V. Monakhov (Russia) Yu. Shokin (Russia) V. Teshukov (Russia) Our thanks are due to the members of the Scientific Com­ mittee, all authors, and participants for contributing to the success of the Conference. We would like to express special appreciation to N. Makarenko, J. Mal'tseva and T. Savelieva, Lavrentyev Institute of Hydrodynamics, for their help in preparing this book for publication.

This book collects research papers presented in the First Franco­ Romanian Conference on Optimization, Optimal Control and Partial Differential Equations held at lasi on 7-11 september 1992. The aim and the underlying idea of this conference was to take advantage of the new SOCial developments in East Europe and in particular in Romania to stimulate the scientific contacts and cooperation between French and Romanian mathematicians and teams working in the field of optimization and partial differential equations. This volume covers a large spectrum of problems and result developments in this field in which most of the participants have brought notable contributions. The following topics are discussed in the contributions presented in this volume. 1 -Variational methods in mechanics and physical models Here we mention the contributions of D. Cioranescu. P. Donato and H.I. Ene (fluid flows in dielectric porous media). R. Stavre (the impact of a jet with two fluids on a porous wall). C. Lefter and D. Motreanu (nonlinear eigenvalue problems with discontinuities). I. Rus (maximum principles for elliptic systems). and on asymptotic XII properties of solutions of evolution equations (R Latcu and M. Megan. R Luca and R Morozanu. R Faure). 2 -The controllabillty of Inflnlte dimensional and distributed parameter systems with the contribution of P. Grisvard (singularities and exact controllability for hyperbolic systems). G. Geymonat. P. Loreti and V. Valente (exact controllability of a shallow shell model). C.

In addition to giving explicit error estimates for partial sums and for interpolating sine polynomials, they also show that Boolean sums yield almost the same asymptotic error estimates as the conventional tensor-product approach, but with a reduced number of terms.

Progress in today's high-technology industries is strongly associated with the development of new mathematical tools. Their contributions, forming the body of this work, cover electric circuit simulation, device simulation and process simulation.

When the first multigrid conference was held in 1981 there was no doubt about the usefulness of a conference dedicated specially to multigrid, because multigrid was a new and relatively unexplored subject, still in a pioneering stage, and pursued by specialists.

The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis.

The book is an outgrowth of the international conference "Centennial Hurwitz on Stability Theory" which was held to honor Adolf Hurwitz, whose arti cle on the location of roots of a polynomial was published one hundred years ago.

New trends in free boundary problems and new mathematical tools together with broadening areas of applications have led to attempts at presenting the state of art of the field in a unified way.

This special volume focuses on optimization and control of processes governed by partial differential equations.

It addresses classical inequalities related to means or to convexity as well as inequalities arising in the field of ordinary and partial differential equations, like Sobolev or Hardy-type inequalities, and inequalities occurring in geometrical contexts.

Leading scientists address current topics such as non-smooth optimization, Hamilton-Jacobi-Bellmann equations, issues in optimization and control of stochastic partial differential equations, reduced-order models and domain decomposition, discretization error estimates for optimal control problems, and control of quantum-dynamical systems.

Nonlinearoptimizationproblemscontainingbothcontinuousanddiscretevariables are called mixed integer nonlinear programs (MINLP). * The MINLP separation and pricing subproblems for generating cuts and columns are solved with specialized MINLP solvers.

Since the seminal work Inequalities (1934) by Hardy, Littlewood and Polya, mathematicians have laboured to extend and sharpen their classical inequalities.

A collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. This welcome reference for many new results and recent methods is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory.

Consisting of 16 refereed contributions, this volume presents a diversified collection of various results in control of distributed parameter systems, including applications in fluid mechanics, partial differential equations, perturbation theory and shape optimization. It is useful for advanced graduate students and researchers.

Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics.

Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics. The mathematical theory of hyperbolic equations has made considerable progress. This set of conference proceedings contains about 100 refereed and selected papers.

Arguably, many industrial optimization problems are of the multiobjective type.

The articles, both theoretical and numerical, encompass a wide range of applications, such as nonlinear waves in solids, various computational fluid dynamics from small-scale combustion to relativistic astrophysical problems, multiphase phenomena and geometrical optics.

A description of the latest and most appropriate mathematical and numerical methods for optimizing soil venting. This book will be of interest to applied mathematicians, geophysicists, geoecologists, soil physicists, and environmental engineers.

Consisting of 23 refereed contributions, this volume offers a broad and diverse view of current research in control and estimation of partial differential equations. Topics addressed include, but are not limited to - control and stability of hyperbolic systems related to elasticity, linear and nonlinear;

The book is an outgrowth of the international conference "Centennial Hurwitz on Stability Theory" which was held to honor Adolf Hurwitz, whose arti cle on the location of roots of a polynomial was published one hundred years ago.

Many phenomena of interest for applications are represented by differential equations which are defined in a domain whose boundary is a priori unknown, and is accordingly named a "free boundary".

This volume contains a collection of papers dealing with applications of orthogonal polynomials and methods for their computation, of interest to a wide audience of numerical analysts, engineers, and scientists. The applications address problems in applied mathematics as well as problems in engineering and the sciences.

Inequalities continue to play an essential role in mathematics. Since the seminal work Inequalities (1934) of Hardy, Littlewood and P6lya mathematicians have laboured to extend and sharpen the earlier classical inequalities.

Numerically oriented articles study finite difference, finite volume, and finite ele ment schemes, adaptive, multiresolution, and artificial dissipation methods.