LEADER 04748nam 2200757 a 450 001 9910781797803321 005 20230725050903.0 010 $a1-283-16682-8 010 $a9786613166821 010 $a3-11-025529-4 024 7 $a10.1515/9783110255294 035 $a(CKB)2550000000042910 035 $a(EBL)797998 035 $a(OCoLC)749781836 035 $a(SSID)ssj0000530409 035 $a(PQKBManifestationID)11339104 035 $a(PQKBTitleCode)TC0000530409 035 $a(PQKBWorkID)10567594 035 $a(PQKB)10842858 035 $a(MiAaPQ)EBC797998 035 $a(WaSeSS)Ind00009646 035 $a(DE-B1597)123627 035 $a(OCoLC)840437417 035 $a(DE-B1597)9783110255294 035 $a(Au-PeEL)EBL797998 035 $a(CaPaEBR)ebr10486432 035 $a(CaONFJC)MIL316682 035 $a(EXLCZ)992550000000042910 100 $a20110224d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBlow-up in nonlinear Sobolev type equations$b[electronic resource] /$fAlexander B. Al?shin, Maxim O. Korpusov, Alexey G. Sveshnikov 210 $aBerlin ;$aNew York $cDe Gruyter$dc2011 215 $a1 online resource (660 p.) 225 1 $aDe Gruyter series in nonlinear analysis and applications,$x0941-8183X ;$v15 300 $aDescription based upon print version of record. 311 $a3-11-025527-8 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tPreface -- $tContents -- $tChapter 0 Introduction -- $tChapter 1 Nonlinear model equations of Sobolev type -- $tChapter 2 Blow-up of solutions of nonlinear equations of Sobolev type -- $tChapter 3 Blow-up of solutions of strongly nonlinear Sobolev-type wave equations and equations with linear dissipation -- $tChapter 4 Blow-up of solutions of strongly nonlinear, dissipative wave Sobolev-type equations with sources -- $tChapter 5 Special problems for nonlinear equations of Sobolev type -- $tChapter 6 Numerical methods of solution of initial-boundary-value problems for Sobolev-type equations -- $tAppendix A Some facts of functional analysis -- $tAppendix B To Chapter 6 -- $tBibliography -- $tIndex 330 $aThe monograph is devoted to the study of initial-boundary-value problems for multi-dimensional Sobolev-type equations over bounded domains. The authors consider both specific initial-boundary-value problems and abstract Cauchy problems for first-order (in the time variable) differential equations with nonlinear operator coefficients with respect to spatial variables. The main aim of the monograph is to obtain sufficient conditions for global (in time) solvability, to obtain sufficient conditions for blow-up of solutions at finite time, and to derive upper and lower estimates for the blow-up time. The abstract results apply to a large variety of problems. Thus, the well-known Benjamin-Bona-Mahony-Burgers equation and Rosenau-Burgers equations with sources and many other physical problems are considered as examples. Moreover, the method proposed for studying blow-up phenomena for nonlinear Sobolev-type equations is applied to equations which play an important role in physics. For instance, several examples describe different electrical breakdown mechanisms in crystal semiconductors, as well as the breakdown in the presence of sources of free charges in a self-consistent electric field. The monograph contains a vast list of references (440 items) and gives an overall view of the contemporary state-of-the-art of the mathematical modeling of various important problems arising in physics. Since the list of references contains many papers which have been published previously only in Russian research journals, it may also serve as a guide to the Russian literature. 410 0$aDe Gruyter series in nonlinear analysis and applications ;$v15. 606 $aInitial value problems$xNumerical solutions 606 $aNonlinear difference equations 606 $aMathematical physics 610 $aBlow up. 610 $aCauchy problem. 610 $aNonlinear equations. 610 $aSobolev. 615 0$aInitial value problems$xNumerical solutions. 615 0$aNonlinear difference equations. 615 0$aMathematical physics. 676 $a515/.782 686 $aSK 540$qSEPA$2rvk 700 $aAl?shin$b A. B$01555395 701 $aKorpusov$b M. O$01034924 701 $aSveshnikov$b A. G$g(Aleksei? 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Many bone disorders arise from the changes that occur in a growing child's musculoskeletal system, and these disorders can positively or negatively impact bone development. Other bone disorders may be inherited or occur in childhood for unknown reasons.Bone disorders in children can result from factors that affect people of all ages, including injury, infection (osteomyelitis), cancer, and metabolic diseases. Causes of bone disorders can involve the gradual misalignment of bones and stress on growth plates during growth. Congenital deformities such as clubfoot or developmental dysplasia of the hip can lead to important alterations of bone development, causing severe dysfunction. Certain rare connective tissue disorders can also affect the bones, such as Marfan syndrome, osteogenesis imperfecta, and osteochondrodysplasias.Many specialists are involved in the management of bone development disorders in children and adolescents, such as neurosurgeons, plastic surgeons, general surgeons, ORL surgeons, maxillofacial surgeons, orthopaedics, radiologists, and pediatric intensive care physicians.The aim of this Special Issue is to present the latest research on the etiology, physiopathology, diagnosis and screening, management, and rehabilitation related to bone development and disease in infants, focusing on congenital, developmental, post-traumatic, and post-infective disorders. 606 $aMedicine and Nursing$2bicssc 610 $abone tumors 610 $abracing 610 $aCervical Vertebral Maturation 610 $achildren 610 $achronological age 610 $aclubfoot 610 $acognitive behavioral therapy 610 $acomplex regional pain syndrome 610 $acomposite prosthesis 610 $acongenital talipes equinovarus 610 $aconservative 610 $aCTEV 610 $aDDH 610 $aDDH prevention 610 $adevelopmental dysplasia of the hip 610 $aDimeglio score 610 $adouple diapering 610 $adrugs 610 $aduration 610 $adynamic splint 610 $aEwing's sarcoma 610 $afracture laterality 610 $agrowing age 610 $ahandedness 610 $ahemophilia 610 $aHerring lateral pillar classification 610 $ahigh-impact sports 610 $ahip adduction 610 $ahip extension 610 $ahip positioning 610 $ahumerus fracture 610 $ainfants 610 $ainterobserver reliability 610 $aLegg-Calve?-Perthes disease 610 $alockdown 610 $amultidisciplinary 610 $an/a 610 $aneonatal hip 610 $aoccupational therapy 610 $apandemic 610 $apediatric 610 $apediatric orthopedics 610 $apharmacological treatment 610 $aphysical activity 610 $aphysical therapy 610 $aPirani score 610 $aponseti method 610 $aprophylaxis 610 $apsychological wellness 610 $areflex sympathetic dystrophy 610 $aSARS-Co-V-2 610 $askeletal maturity 610 $asport 610 $asport activity level 610 $asport practice 610 $astatic splint 610 $aStulberg classification 610 $asupracondylar humerus fracture 610 $atrauma 610 $atreatment 610 $aupper limb fracture 610 $aWaldenstro?m stage 610 $ayoung athletes 615 7$aMedicine and Nursing 700 $aPavone$b Vito$4edt$01296675 702 $aPavone$b Vito$4oth 906 $aBOOK 912 $a9910576883803321 996 $aBone Development and Disease in Infants$93024208 997 $aUNINA