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Exact solutions and invariant subspaces of nonlinear partial differential equations in mechanics and physics par Galaktionov,, Victor A. Publication : [S.l.] Chapman and Hall/CRC 2006 . 528 p. , Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties. This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders. The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types. 24 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Finite element methods and their applications / par Chen,, Zhangxin, Publication : Berlin ; | New York : Springer, 2005 . xiii, 410 p. : 25 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Foundations of the classical theory of partial differential equations par Egorov, Yu.V. Publication : [S.l.] Springer 1998 . 259 p. , From the reviews: "...I think the volume is a great success ... a welcome addition to the literature ..." The Mathematical Intelligencer, 1993 "... It is comparable in scope with the great Courant-Hilbert Methods of Mathematical Physics, but it is much shorter, more up to date of course, and contains more elaborate analytical machinery...." The Mathematical Gazette, 1993. 24 cm. Date : 1998 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Geometric theory of incompressible flows with applications to fluid dynamics / par Ma,, Tian, Publication : Providence, RI : American Mathematical Society, 2005 . ix, 234 p. : 26 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Gradient flows in metric spaces and in the space of probability measures / par Ambrosio,, Luigi. Publication : [berlin.] Birkhuser Basel 2005 . 341 p. , The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other. 24 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Iterative methods for sparse linear systems / par Saad,, Y. Publication : Philadelphia : SIAM, 2003 . xviii, 528 p. : 25 cm. Date : 2003 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Lectures on Probability Theory and Statistics : Ecole d'été de Probabilités de Saint-Flour XXXIII - 2003 / par Picard, Jean, Publication : Berlin Heidelberg : Springer-Verlag., 2005 . 1 online resource. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Methods of nonlinear analysis applications to differential equations par Dràbek, Pavel Publication : Basel | Boston | Berlin Birkhäuser 2007 . 568 p. , In this book, the basic methods of nonlinear analysis are emphasized and illustrated in simple examples. Every considered method is motivated, explained in a general form but in the simplest possible abstract framework. Its applications are shown, particularly to boundary value problems for elementary ordinary or partial differential equations. The text is organized in two levels: a self-contained basic and, organized in appendices, an advanced level for the more experienced reader. Exercises are an organic part of the exposition and accompany the reader throughout the book. 24 cm. Date : 2007 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Multiscale methods : averaging and homogenization / par Pavliotis, Grigorios A. Publication : New York : Springer, 2008 . xviii, 307 pages : 25 cm. Date : 2008 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Nodal discontinuous Galerkin methods : algorithms, analysis, and applications / par Hesthaven, Jan S. Publication : New York : Springer, 2008 . xiv, 500 pages : 25 cm. Date : 2008 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Numerical methods for elliptic and parabolic partial differential equations / par Knabner, Peter. Publication : New York : Springer, 2003 . xv, 424 p. : 25 cm. Date : 2003 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Partial differential equations par Bitsadze, A V. Publication : Singapore World Scientific 1994 . 227 p. , This textbook in partial differential equations has been adopted as course material by the Moscow State University. The theoretical foundations of Pde are explained rigorously and clearly in such a way that their importance on applications is also taken into account. The presentation of materials has been arranged to be conducive to promoting students' interest in mathematical experiments. 22 cm. Date : 1994 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Partial differential equations / par John,, Fritz, Publication : New York : Springer-Verlag, 1982 . x, 249 p. : , Includes index. 25 cm. Date : 1982 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Partial differential equations par Sauvigny,, Friedrich. Publication : Berlin Springer 2006 . 2 volumes , Expanded version of the German original edition. 24 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Partial differential equations par Jost, Jürgen Publication : New York Springer 2013 . xiii, 410 pages 25 cm. Date : 2013 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Postmodern analysis par Jost, Jürgen. Publication : Berlin ; New York Springer 2005 . 371 p , This is an introduction to advanced analysis at the beginning graduate level that blends a modern presentation with concrete examples and applications, in particular in the areas of calculus of variations and partial differential equations. The book does not strive for abstraction for its own sake, but tries rather to impart a working knowledge of the key methods of contemporary analysis, in particular those that are also relevant for application in physics. It provides a streamlined and quick introduction to the fundamental concepts of Banach space and Lebesgue integration theory and the basic notions of the calculus of variations, including Sobolev space theory. The third edition contains new material on further important tool in analysis, namely cover theorems. Useful references for such results and further properties of various classes of weakly differential functions are added. And finally, misprints and minor inconsistencies have been corrected. 24 cm. Date : 2005 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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