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In this volume, Olga A. Ladyzhenskaya expands on her highly successful 1991 Accademia Nazionale dei Lincei lectures. The lectures were devoted to questions of the behaviour of trajectories for semigroups of nonlinear bounded continuous operators in a locally non-compact metric space and for solutions of abstract evolution equations. The latter contain many initial boundary value problems for dissipative partial differential equations. This work, for which Ladyzhenskaya was awarded the Russian Academy of Sciences' Kovalevskaya Prize, reflects the high calibre of her lectures; it is essential reading for anyone interested in her approach to partial differential equations and dynamical systems. This edition, reissued for her centenary, includes a new technical introduction, written by Gregory A. Seregin, Varga K. Kalantarov and Sergey V. Zelik, surveying Ladyzhenskaya's works in the field and subsequent developments influenced by her results.
Semigroups of operators. --- Evolution equations. --- Attractors (Mathematics)
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This book presents an expansion of the highly successful lectures given by Professor Ladyzhenskaya at the University of Rome, 'La Sapienza', under the auspices of the Accademia dei Lencei. The lectures were devoted to questions of the behaviour of trajectories for semi-groups of non-linear bounded continuous operators in a locally non-compact metric space and for solutions of abstract evolution equations. The latter contain many boundaries value problems for partial differential equations of a dissipative type. Professor Ladyzhenskaya was an internationally renowned mathematician and her lectures attracted large audiences. These notes reflect the high calibre of her lectures and should prove essential reading for anyone interested in partial differential equations and dynamical systems.
Semigroups of operators. --- Evolution equations. --- Attractors (Mathematics)
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Semigroups of operators --- Evolution equations --- Attractors (Mathematics) --- Semigroups of operators. --- Evolution equations. --- Attractors (mathematics)
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Problems, ideas and notions from the theory of finite-dimensional dynamical systems have penetrated deeply into the theory of infinite-dimensional systems and partial differential equations. From the standpoint of the theory of the dynamical systems, many scientists have investigated the evolutionary equations of mathematical physics. Such equations include the Navier-Stokes system, magneto-hydrodynamics equations, reaction-diffusion equations, and damped semilinear wave equations. Due to the recent efforts of many mathematicians, it has been established that the attractor of the Navier-Stokes
Navier-Stokes equations --- Attractors (Mathematics) --- Numerical solutions. --- Numerical solutions
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This book grew out of the work developed at the University of Warwick, under the supervision of Ian Stewart, which formed the core of my Ph.D. Thesis. Most of the results described were obtained in joint work with Ian; as usual under these circumstances, many have been published in research journals over the last two years. Part of Chapter 3 was also joint work with Peter Ashwin. I would like to stress that these were true collaborations. We worked together at all stages; it is meaningless to try to identify which idea originated from whom. While preparing this book, however, I felt that a mere description of the results would not be fitting. First of all, a book is aimed at a wider audience than papers in research journals. More importantly, the work should assume as little as possible, and it should be brought to a form which is pleasurable, not painful, to read.
Differential geometry. Global analysis --- Attractors (Mathematics) --- Attractors (Mathematics). --- Topology. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear
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This book, based on lectures given at the Accademia dei Lincei, is an accessible and leisurely account of systems that display a chaotic time evolution. This behaviour, though deterministic, has features more characteristic of stochastic systems. The analysis here is based on a statistical technique known as time series analysis and so avoids complex mathematics, yet provides a good understanding of the fundamentals. Professor Ruelle is one of the world's authorities on chaos and dynamical systems and his account here will be welcomed by scientists in physics, engineering, biology, chemistry and economics who encounter nonlinear systems in their research.
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Chaotic behavior in systems --- Attractors (Mathematics) --- Topology --- Chaos --- Attracteurs (Mathématiques) --- Topologie
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Problems, ideas and notions from the theory of finite-dimensional dynamical systems have penetrated deeply into the theory of infinite-dimensional systems and partial differential equations. From the standpoint of the theory of the dynamical systems, many scientists have investigated the evolutionary equations of mathematical physics. Such equations include the Navier-Stokes system, magneto-hydrodynamics equations, reaction-diffusion equations, and damped semilinear wave equations. Due to the recent efforts of many mathematicians, it has been established that the attractor of the Navier-Stokes
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