04002nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001700186072002300203082001600226100002900242245011700271264006700388300003500455336002600490337002600516338003600542347002400578490005300602505058600655520169201241650001702933650001402950650002002964650003602984650002503020650001703045650003603062650002403098650004203122700003103164710003403195773002003229776003603249830005303285856004803338912001403386999001903400952007703419978-1-4614-6995-7DE-He21320180115171528.0cr nn 008mamaa130606s2013 xxu| s |||| 0|eng d a97814614699579978-1-4614-6995-77 a10.1007/978-1-4614-6995-72doi 4aQA370-380 7aPBKJ2bicssc 7aMAT0070002bisacsh04a515.3532231 aKapitula, Todd.eauthor.10aSpectral and Dynamical Stability of Nonlinear Wavesh[electronic resource] /cby Todd Kapitula, Keith Promislow. 1aNew York, NY :bSpringer New York :bImprint: Springer,c2013. aXIII, 361 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aApplied Mathematical Sciences,x0066-5452 ;v1850 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. . 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. 0aMathematics. 0aDynamics. 0aErgodic theory. 0aPartial differential equations. 0aStatistical physics.14aMathematics.24aPartial Differential Equations.24aNonlinear Dynamics.24aDynamical Systems and Ergodic Theory.1 aPromislow, Keith.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9781461469940 0aApplied Mathematical Sciences,x0066-5452 ;v18540uhttp://dx.doi.org/10.1007/978-1-4614-6995-7 aZDB-2-SMA c370732d370732 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK