000 03928nam a22004815i 4500
001 978-1-4614-6995-7
003 DE-He213
005 20140220082827.0
007 cr nn 008mamaa
008 130606s2013 xxu| s |||| 0|eng d
020 _a9781461469957
_9978-1-4614-6995-7
024 7 _a10.1007/978-1-4614-6995-7
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aKapitula, Todd.
_eauthor.
245 1 0 _aSpectral and Dynamical Stability of Nonlinear Waves
_h[electronic resource] /
_cby Todd Kapitula, Keith Promislow.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXIII, 361 p. 50 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v185
505 0 _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.
520 _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.
650 0 _aMathematics.
650 0 _aDifferentiable dynamical systems.
650 0 _aDifferential equations, partial.
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aNonlinear Dynamics.
650 2 4 _aDynamical Systems and Ergodic Theory.
700 1 _aPromislow, Keith.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461469940
830 0 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v185
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-6995-7
912 _aZDB-2-SMA
999 _c95817
_d95817