01171cam0 22003011 450 SOBE0007680620230726123206.020230726d2017 |||||ita|0103 baitaITEnchanted AnguishSalvatore Violante; with introductory notes by Marcello Carlino and Wanda Marascotranslated by Lina Sanniti and Michael PalmaNew YorkGradiva Publicationsc201775 p.14 cmEnchanted AnguishSOBA000281623399452Violante, Salvatore <1943->SOBA000281610701370941Carlino, MarcelloAF00024537070Marasco, WandaSOBA00000577070Palma, MichaelSOBA00028160070Sanniti, LinaSOBA00028159070ITUNISOB20230726RICAUNISOBUNISOBFondo|Durante179705SOBE00076806M 102 Monografia moderna SBNMFondo|Durante000486SI1797052023060660DurantedonoN60bethbUNISOBUNISOB20230726123125.020230726123206.0bethbEnchanted Anguish3399452UNISOB05024nam 22007575 450 991043815310332120200629210849.01-4614-6995-310.1007/978-1-4614-6995-7(CKB)2670000000393916(EBL)1317310(OCoLC)854975791(SSID)ssj0000936117(PQKBManifestationID)11536168(PQKBTitleCode)TC0000936117(PQKBWorkID)10961376(PQKB)10533913(DE-He213)978-1-4614-6995-7(MiAaPQ)EBC6315790(MiAaPQ)EBC1317310(Au-PeEL)EBL1317310(CaPaEBR)ebr10965889(PPN)17048825X(EXLCZ)99267000000039391620130606d2013 u| 0engur|n|---|||||txtccrSpectral and Dynamical Stability of Nonlinear Waves /by Todd Kapitula, Keith Promislow1st ed. 2013.New York, NY :Springer New York :Imprint: Springer,2013.1 online resource (368 p.)Applied Mathematical Sciences,0066-5452 ;185Description based upon print version of record.1-4939-0187-7 1-4614-6994-5 Includes bibliographical references (pages 345-357) and index.Introduction -- 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.    .This 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.Applied Mathematical Sciences,0066-5452 ;185Partial differential equationsStatistical physicsDynamicsErgodic theoryPartial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Applications of Nonlinear Dynamics and Chaos Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/P33020Dynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XPartial differential equations.Statistical physics.Dynamics.Ergodic theory.Partial Differential Equations.Applications of Nonlinear Dynamics and Chaos Theory.Dynamical Systems and Ergodic Theory.515.353Kapitula Toddauthttp://id.loc.gov/vocabulary/relators/aut521430Promislow Keithauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910438153103321Spectral and Dynamical Stability of Nonlinear Waves2534287UNINA