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Selected Works of Jindřich Nečas
The book collects the most significant contributions of the outstanding Czech mathematician Jindřich Nečas, who was honoured with the Order of Merit of the Czech Republic by President Václav Havel. Starting with Nečas’s brief biography and short comments on his role in the beginnings of modern PDE research in Prague, the book then follows the periods of his research career. The first part is devoted to the linear theory of partial differential equations. Its topics include the variational approach to linear boundary value problems and the Rellich - Nečas inequalities, together with their applications to boundary regularity. The second part is concerned with the regularity for nonlinea...
Direct Methods in the Theory of Elliptic Equations
Nečas’ book Direct Methods in the Theory of Elliptic Equations, published 1967 in French, has become a standard reference for the mathematical theory of linear elliptic equations and systems. This English edition, translated by G. Tronel and A. Kufner, presents Nečas’ work essentially in the form it was published in 1967. It gives a timeless and in some sense definitive treatment of a number issues in variational methods for elliptic systems and higher order equations. The text is recommended to graduate students of partial differential equations, postdoctoral associates in Analysis, and scientists working with linear elliptic systems. In fact, any researcher using the theory of ellipt...
Direct Methods in the Theory of Elliptic Equations
Nečas’ book Direct Methods in the Theory of Elliptic Equations, published 1967 in French, has become a standard reference for the mathematical theory of linear elliptic equations and systems. This English edition, translated by G. Tronel and A. Kufner, presents Nečas’ work essentially in the form it was published in 1967. It gives a timeless and in some sense definitive treatment of a number issues in variational methods for elliptic systems and higher order equations. The text is recommended to graduate students of partial differential equations, postdoctoral associates in Analysis, and scientists working with linear elliptic systems. In fact, any researcher using the theory of ellipt...
Applied Nonlinear Analysis
Proceedings of an International Workshop on Nonlinear PDEs and Applications, held December 13-17, 1999, in Olomouc, Czech Republic, in honour of the 70th birthday of Professor Jindrich Necas
Solution of Variational Inequalities in Mechanics
The idea for this book was developed in the seminar on problems of con tinuum mechanics, which has been active for more than twelve years at the Faculty of Mathematics and Physics, Charles University, Prague. This seminar has been pursuing recent directions in the development of mathe matical applications in physics; especially in continuum mechanics, and in technology. It has regularly been attended by upper division and graduate students, faculty, and scientists and researchers from various institutions from Prague and elsewhere. These seminar participants decided to publish in a self-contained monograph the results of their individual and collective efforts in developing applications for ...
Partial Differential Equations
As a satellite conference of the 1998 International Mathematical Congress and part of the celebration of the 650th anniversary of Charles University, the Partial Differential Equations Theory and Numerical Solution conference was held in Prague in August, 1998. With its rich scientific program, the conference provided an opportunity for almost 200 participants to gather and discuss emerging directions and recent developments in partial differential equations (PDEs). This volume comprises the Proceedings of that conference. In it, leading specialists in partial differential equations, calculus of variations, and numerical analysis present up-to-date results, applications, and advances in nume...
Advances in Mathematical Fluid Mechanics
This book consists of six survey contributions that are focused on several open problems of theoretical fluid mechanics both for incompressible and compressible fluids. The first article "Viscous flows in Besov spaces" by M area Cannone ad dresses the problem of global existence of a uniquely defined solution to the three-dimensional Navier-Stokes equations for incompressible fluids. Among others the following topics are intensively treated in this contribution: (i) the systematic description of the spaces of initial conditions for which there exists a unique local (in time) solution or a unique global solution for small data, (ii) the existence of forward self-similar solutions, (iii) the r...
Mathematical Theory in Fluid Mechanics
This volume consists of four contributions that are based on a series of lectures delivered by Jens Frehse. Konstantin Pikeckas, K.R. Rajagopal and Wolf von Wahl t the Fourth Winter School in Mathematical Theory in Fluid Mechanics, held in Paseky, Czech Republic, from December 3-9, 1995. In these papers the authors present the latest research and updated surveys of relevant topics in the various areas of theoretical fluid mechanics. Specifically, Frehse and Ruzicka study the question of the existence of a regular solution to Navier-Stokes equations in five dimensions by means of weighted estimates. Pileckas surveys recent results regarding the solvability of the Stokes and Navier-Stokes syst...
Progress in Theoretical and Computational Fluid Mechanics
This volume presents a series of lectures given at the Winter School in Fluid Dynamics held in Paseky, Czech Republic in December 1993. Including original research and important new results, it contains a detailed investigation of some methods used towards the proof of global regularity for the Navier-Stokes equations. It also explores new formulations of the free-boundary in the dynamics of viscous fluids, and different methods for conservation laws in several space dimensions and related numerical schemes. The final contribution examines the existence and stability of non-isothermal compressible fluids and their relation with incompressible models.
