Inverse Problems for Kinetic and Other Evolution Equations PDF Download
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Author: Yu. E. Anikonov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110940906
Category : Mathematics
Languages : en
Pages : 280
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Book Description
This monograph deals with methods of studying multidimensional inverse problems for kinetic and other evolution equations, in particular transfer equations. The methods used are applied to concrete inverse problems, especially multidimensional inverse problems applicable in linear and nonlinear statements. A significant part of the book contains formulas and relations for solving inverse problems, including formulas for the solution and coefficients of kinetic equations, differential-difference equations, nonlinear evolution equations, and second order equations.
Author: Yu. E. Anikonov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110940906
Category : Mathematics
Languages : en
Pages : 280
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Book Description
This monograph deals with methods of studying multidimensional inverse problems for kinetic and other evolution equations, in particular transfer equations. The methods used are applied to concrete inverse problems, especially multidimensional inverse problems applicable in linear and nonlinear statements. A significant part of the book contains formulas and relations for solving inverse problems, including formulas for the solution and coefficients of kinetic equations, differential-difference equations, nonlinear evolution equations, and second order equations.
Author: Alexander L. Sakhnovich
Publisher: Walter de Gruyter
ISBN: 3110258617
Category : Mathematics
Languages : en
Pages : 356
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Book Description
This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund–Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses.
Author: I︠U︡riĭ Evgenʹevich Anikonov
Publisher: VSP
ISBN: 9789067643450
Category : Mathematics
Languages : en
Pages : 288
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Book Description
This monograph in the "Inverse and Ill-Posed Problems Series deals with methods of studying multidimensional inverse problems for kinetic and other evolution equations, in particular transfer equations. The methods used are applied to concrete inverse problems, especially multidimensional inverse problems applicable in linear and nonlinear statements.A significant part of the book contains formulas and relations for solving inverse problems, including formulas for the solution and coefficients of kinetic equations, differential-difference equations, nonlinear evolution equations, and second order equations.This monograph will be of value and interest to mathematicians, engineers and other specialists dealing with inverse and ill posed problems.
Author: Mark J. Ablowitz
Publisher: Cambridge University Press
ISBN: 0521387302
Category : Mathematics
Languages : en
Pages : 532
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Book Description
This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.
Author: Centre national de la recherche scientifique (France). Recherche coopérative sur programme 264
Publisher: Centre National de la Recherche Scientifique
ISBN:
Category : Evolution equations
Languages : en
Pages : 304
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Book Description
Author: J. Kral
Publisher: Springer Science & Business Media
ISBN: 1461344255
Category : Mathematics
Languages : en
Pages : 138
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Book Description
Preface.- Gottfried Anger: Direct and inverse problems in potential theory.- Viorel Barbu: Regularity results for sane differential equations associated with maximal monotone operators in Hilbert spaces.- Haim Brezis: Classes d'interpolation associées à un opérateur monotone et applications.- Siegfried Dnümmel: On inverse problems for k-dimensional potentials.- Jozef Ka?ur: Application of Rothe's method to nonlinear parabolic boundary value problems.- Josef Král: Potentials and removability of singularities.- Vladimir Lovicar: Theorem of Fréchet and asymptotically almost periodid solutions of.
Author: Sandra Carillo
Publisher: Springer Science & Business Media
ISBN: 3642840396
Category : Science
Languages : en
Pages : 247
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Book Description
Nonlinear Evolution Equations and Dynamical Systems (NEEDS) provides a presentation of the state of the art. Except for a few review papers, the 40 contributions are intentially brief to give only the gist of the methods, proofs, etc. including references to the relevant litera- ture. This gives a handy overview of current research activities. Hence, the book should be equally useful to the senior resercher as well as the colleague just entering the field. Keypoints treated are: i) integrable systems in multidimensions and associated phenomenology ("dromions"); ii) criteria and tests of integrability (e.g., Painlev test); iii) new developments related to the scattering transform; iv) algebraic approaches to integrable systems and Hamiltonian theory (e.g., connections with Young-Baxter equations and Kac-Moody algebras); v) new developments in mappings and cellular automata, vi) applications to general relativity, condensed matter physics, and oceanography.
Author: Vladimir G. Makhankov
Publisher: Springer Science & Business Media
ISBN: 3642761720
Category : Science
Languages : en
Pages : 256
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Book Description
Proceedings of the 6th International Workshop, 16-26 July 1990, Dubna, USSR
Author: Antonio Degasperis
Publisher:
ISBN:
Category : Evolution equations, Nonlinear
Languages : en
Pages : 648
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Book Description
Author: Robert M. Conte
Publisher: Springer Science & Business Media
ISBN: 9783540200871
Category : Science
Languages : en
Pages : 306
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Book Description
Many physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical methods, presented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable equations. The direct method to build solutions includes the analysis of singularities à la Painlevé, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition formula. The main inverse method described here relies on the bi-hamiltonian structure of integrable equations. The book also presents some extension to equations with discrete independent and dependent variables. The different chapters face from different points of view the theory of exact solutions and of the complete integrability of nonlinear evolution equations. Several examples and applications to concrete problems allow the reader to experience directly the power of the different machineries involved.
