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Sveshnikov vs the Anti-Sicilians
The Sicilian Defence is Black’s most popular reply to 1.e4. Most black players hope to get an Open Sicilian because of its unbalanced play and interesting opportunities to play for a win. But what if White avoids the Open Sicilian and does not play 2.Nf3? This happens more often than you would think, as in roughly one third of the cases White players opt for one of the numerous ‘Anti-Sicilian’ lines at their disposal. These Anti-Sicilians vary from primitive and obscure to wild and aggressive to respected but tedious. But they have one thing in common: they are all dragging Black into territory where he doesn’t want to be, and where it is easy to get ambushed. Evgeny Sveshnikov offers help. The Russian grandmaster, who is one of the most respected chess opening experts in the world, presents practical and effective recipes against a broad range of annoying variations: 2.a3?, 2.Na3?!, 2.b4?!, 2.b3, 2.Nc3, 2.d3 and many others. Black players will learn how to fight back and throw a spanner in the works when White tries to spoil their game.
Blow-Up in Nonlinear Equations of Mathematical Physics
The present book carefully studies the blow-up phenomenon of solutions to partial differential equations, including many equations of mathematical physics. The included material is based on lectures read by the authors at the Lomonosov Moscow State University, and the book is addressed to a wide range of researchers and graduate students working in nonlinear partial differential equations, nonlinear functional analysis, and mathematical physics. Contents Nonlinear capacity method of S. I. Pokhozhaev Method of self-similar solutions of V. A. Galaktionov Method of test functions in combination with method of nonlinear capacity Energy method of H. A. Levine Energy method of G. Todorova Energy method of S. I. Pokhozhaev Energy method of V. K. Kalantarov and O. A. Ladyzhenskaya Energy method of M. O. Korpusov and A. G. Sveshnikov Nonlinear Schrödinger equation Variational method of L. E. Payne and D. H. Sattinger Breaking of solutions of wave equations Auxiliary and additional results
The Complete French Advance
The Advance Variation is the most ambitious way to meet the solid French Defence. Its popularity among club players is not difficult to understand: by advancing the e-pawn to e5 on the third move, White not only gains space but also blocks in Black’s c8 Bishop and hampers Black’s kingside development by taking away the f6-square. The closed nature of the positions arising from the Advance Variation leads to strategic play where positional understanding is much more important than studying the latest theoretical developments. White can use the advantage in space by building up an attack against the Black king. Grandmaster Evgeny Sveshnikov has played the Advance Variation in countless gam...
Blow-up in Nonlinear Sobolev Type Equations
The monograph is devoted to the study of initial-boundary-value problems for multi-dimensional Sobolev-type equations over bounded domains. The authors consider both specific initial-boundary-value problems and abstract Cauchy problems for first-order (in the time variable) differential equations with nonlinear operator coefficients with respect to spatial variables. The main aim of the monograph is to obtain sufficient conditions for global (in time) solvability, to obtain sufficient conditions for blow-up of solutions at finite time, and to derive upper and lower estimates for the blow-up time. The abstract results apply to a large variety of problems. Thus, the well-known Benjamin-Bona-Ma...
The Complete Sveshnikov Sicilian
The Sveshnikov Variation is one of the most uncompromising lines of the Sicilian Defence. Black accepts an apparently loose pawn-structure in return for a great deal of piece activity. Decades of experience have shown that it is far from easy for White to neutralize Black's active play, and the Sveshnikov is now firmly established as a favourite weapon for players who wish to win games as Black. Leading grandmasters who have relied on the Sveshnikov include John Nunn, Michal Krasenkow, Joel Lautier, Miguel Illescas, Alexei Shirov, Peter Leko and, most notably, BGN World Champion Vladimir Kramnik.
The Sveshnikov Sicilian
Grandmaster Mikhail Krasenkov is one of the leading experts on the Sveshnikov variation of the Sicilian Defense, one of the shaprest and most combative of all chess openings. Krasenkov, also author of the bestselling The Open Spanish, discusses the main ideas of the Sveshnikov Sicilian and provides a highly instructive selection of illustrative games to explain the key ideas.
Blow-up in Nonlinear Sobolev Type Equations
The monograph is devoted to the study of initial-boundary-value problems for multi-dimensional Sobolev-type equations over bounded domains. The authors consider both specific initial-boundary-value problems and abstract Cauchy problems for first-order (in the time variable) differential equations with nonlinear operator coefficients with respect to spatial variables. The main aim of the monograph is to obtain sufficient conditions for global (in time) solvability, to obtain sufficient conditions for blow-up of solutions at finite time, and to derive upper and lower estimates for the blow-up time. The monograph contains a vast list of references (440 items) and gives an overall view of the contemporary state-of-the-art of the mathematical modeling of various important problems arising in physics. Since the list of references contains many papers which have been published previously only in Russian research journals, it may also serve as a guide to the Russian literature.
Strongly Coupled Parabolic and Elliptic Systems
Strongly coupled (or cross-diffusion) systems of parabolic and elliptic partial differential equations appear in many physical applications. This book presents a new approach to the solvability of general strongly coupled systems, a much more difficult problem in contrast to the scalar case, by unifying, elucidating and extending breakthrough results obtained by the author, and providing solutions to many open fundamental questions in the theory. Several examples in mathematical biology and ecology are also included. Contents Interpolation Gagliardo–Nirenberg inequalities The parabolic systems The elliptic systems Cross-diffusion systems of porous media type Nontrivial steady-state solutions The duality RBMO(μ)–H1(μ)| Some algebraic inequalities Partial regularity
Periodic Differential Equations in the Plane
Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is based on the introduction of small parameters, but the search of nonlocal results leads to the application of several topological tools. Examples are fixed point theorems, degree theory, or bifurcation theory. These well-known methods are valid for equations of arbitrary dimension and they are mainly employed to prove the existence of periodic solutions. Following the approach initiated by Massera, this book presents some more delicate techniques whose validity...
Morse Index of Solutions of Nonlinear Elliptic Equations
This monograph presents in a unified manner the use of the Morse index, and especially its connections to the maximum principle, in the study of nonlinear elliptic equations. The knowledge or a bound on the Morse index of a solution is a very important qualitative information which can be used in several ways for different problems, in order to derive uniqueness, existence or nonexistence, symmetry, and other properties of solutions.
