LEADER 04638nam 2200601 450 001 9910786641803321 005 20230120014536.0 010 $a1-4831-5454-8 035 $a(CKB)3710000000199928 035 $a(EBL)1901292 035 $a(SSID)ssj0001433200 035 $a(PQKBManifestationID)11791190 035 $a(PQKBTitleCode)TC0001433200 035 $a(PQKBWorkID)11413777 035 $a(PQKB)11520030 035 $a(MiAaPQ)EBC1901292 035 $a(EXLCZ)993710000000199928 100 $a20150122h19821982 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aDifferential equations and numerical mathematics $eselected papers presented to a national conference held in Novosibirsk, September 1978 /$fedited by G. I. Marchuk 205 $aFirst English edition. 210 1$aOxford, England :$cPergamon Press,$d1982. 210 4$dİ1982 215 $a1 online resource (165 p.) 300 $aDescription based upon print version of record. 311 $a1-322-55610-5 311 $a0-08-026491-3 320 $aIncludes bibliographical references at the end of each chapters. 327 $aFront Cover; Differential Equations and Numerical Mathematics; Copyright Page; Preface; Table of Contents; SECTION A: Cubature Formulae and Functional Analysis; CHAPTER 1. On an analogue of Plancherel's theorem and on the qualitative character of the spectrum of a self-adjoint operator; References; References; CHAPTER 2. Self-adjoint operators in spaces of functions of an infinite number of variables; CHAPTER 3. Multidimensional non-linear spectral boundary value problems and soliton superposition of their asymptotic solutions; 1. A non-linear spectral boundary value problem of Steklov type 327 $a2. Asymptotic complex-valued solutions, concentrated in the neighbourhood of closed geodesies3. ""Non-linear superposition"" of asymptotic solutions, multidimensional Dirichlet series and real-valued asymptotic solutions; 4. Example; 5. Problem of reflection from a boundary and finite-gap almost periodic solutions; References; CHAPTER 4. Re?duction de la dimension dans un proble?me de contro?le optimal; Introduction; 1. Position du proble?me; 2. Enonce du re?sultat; 3. Bornes supe?rieures; 4. Dualite?; 5. Bornes infe?rieures; Re?fe?rences 327 $a2. The second asymptotic formula3. The domain of validity of formula II; 4. The magnitude of qlIj{k) and the error for large values of q; 5. The first asymptotic formula; 6. Estimation of ?; 7. The estimation of ?1; 8. The estimation of ?2; 9. The estimation of the error of formula I; 10. The estimation of the length of productive intervals for q = 0(k-1/2); References; CHAPTER 8. On certain mathematical problems in hydrodynamics; 1. On the approximation of solenoidal vector fields 327 $a2. The second problem we should like to consider is the investigation of the decay and rise of vorticity in a moving continuous mediumReferences; CHAPTER 9. On the solvability of the Sturm-Liouville inverse problem on the entire line; 1. Solution of the inverse problem on the entire line by a spectral matrix function; 2. Application to the Korteveg-de Vries equation; References; CHAPTER 10. Asymptotic properties of solutions of partial differential equations; References; CHAPTER 11. Boundary value problems for weakly elliptic systems of differential equations; References 327 $aSECTION C: Numerical Mathematics 330 $aDifferential Equations and Numerical Mathematics contains selected papers presented in a national conference held in Novosibirsk on September 1978. This book, as the conference, is organized into three sections. Section A describes the modern theory of efficient cubature formulas; embedding theorems; and problems of spectral analysis. Section B considers the theoretical questions of partial differential equations, with emphasis on hyperbolic equations and systems, formulations, and methods for nonclassical problems of mathematical physics. Section C addresses the various problems of numerical 606 $aDifferential equations 606 $aNumerical analysis 606 $aFunctional analysis 615 0$aDifferential equations. 615 0$aNumerical analysis. 615 0$aFunctional analysis. 676 $a515.3/5 702 $aMarchuk$b G. I$g(Gurii? Ivanovich),$f1925- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910786641803321 996 $aDifferential equations and numerical mathematics$9436795 997 $aUNINA