LEADER 05024nam 22007575 450 001 9910438153103321 005 20200629210849.0 010 $a1-4614-6995-3 024 7 $a10.1007/978-1-4614-6995-7 035 $a(CKB)2670000000393916 035 $a(EBL)1317310 035 $a(OCoLC)854975791 035 $a(SSID)ssj0000936117 035 $a(PQKBManifestationID)11536168 035 $a(PQKBTitleCode)TC0000936117 035 $a(PQKBWorkID)10961376 035 $a(PQKB)10533913 035 $a(DE-He213)978-1-4614-6995-7 035 $a(MiAaPQ)EBC6315790 035 $a(MiAaPQ)EBC1317310 035 $a(Au-PeEL)EBL1317310 035 $a(CaPaEBR)ebr10965889 035 $a(PPN)17048825X 035 $a(EXLCZ)992670000000393916 100 $a20130606d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSpectral and Dynamical Stability of Nonlinear Waves /$fby Todd Kapitula, Keith Promislow 205 $a1st ed. 2013. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2013. 215 $a1 online resource (368 p.) 225 1 $aApplied Mathematical Sciences,$x0066-5452 ;$v185 300 $aDescription based upon print version of record. 311 $a1-4939-0187-7 311 $a1-4614-6994-5 320 $aIncludes bibliographical references (pages 345-357) and index. 327 $aIntroduction -- Background material and notation -- Essential and absolute spectra -- Dynamical implications of spectra: dissipative systems -- Dynamical implications of spectra: Hamiltonian systems -- Dynamical implications of spectra: Hamiltonian systems -- Point spectrum: reduction to finite-rank eigenvalue problems -- Point spectrum: linear Hamiltonian systems -- The Evans function for boundary value problems -- The Evans function for Sturm-Liouville operators on the real line -- The Evans function for nth-order operators on the real line -- Index -- References.    . 330 $aThis book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates and methodically develops key ideas by working through illustrative examples that are subsequently synthesized into general principles. Many of the seminal examples of stability theory, including orbital stability of the KdV solitary wave, and asymptotic stability of viscous shocks for scalar conservation laws, are treated in a textbook fashion for the first time. It presents spectral theory from a dynamical systems and functional analytic point of view, including essential and absolute spectra, and develops general nonlinear stability results for dissipative and Hamiltonian systems. The structure of the linear eigenvalue problem for Hamiltonian systems is carefully developed, including the Krein signature and related stability indices. The Evans function for the detection of point spectra is carefully developed through a series of frameworks of increasing complexity. Applications of the Evans function to the Orientation index, edge bifurcations, and large domain limits are developed through illustrative examples. The book is intended for first or second year graduate students in mathematics, or those with equivalent mathematical maturity. It is highly illustrated and there are many exercises scattered throughout the text that highlight and emphasize the key concepts. Upon completion of the book, the reader will be in an excellent position to understand and contribute to current research in nonlinear stability. 410 0$aApplied Mathematical Sciences,$x0066-5452 ;$v185 606 $aPartial differential equations 606 $aStatistical physics 606 $aDynamics 606 $aErgodic theory 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aApplications of Nonlinear Dynamics and Chaos Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P33020 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 615 0$aPartial differential equations. 615 0$aStatistical physics. 615 0$aDynamics. 615 0$aErgodic theory. 615 14$aPartial Differential Equations. 615 24$aApplications of Nonlinear Dynamics and Chaos Theory. 615 24$aDynamical Systems and Ergodic Theory. 676 $a515.353 700 $aKapitula$b Todd$4aut$4http://id.loc.gov/vocabulary/relators/aut$0521430 702 $aPromislow$b Keith$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438153103321 996 $aSpectral and Dynamical Stability of Nonlinear Waves$92534287 997 $aUNINA