LEADER 03106nam 22003975a 450 001 9910151928703321 005 20110729234510.0 010 $a3-03719-595-9 024 70$a10.4171/095 035 $a(CKB)3710000000953871 035 $a(CH-001817-3)134-110729 035 $a(PPN)178155969 035 $a(EXLCZ)993710000000953871 100 $a20110729j20110902 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aInvariant Manifolds and Dispersive Hamiltonian Evolution Equations$b[electronic resource] /$fKenji Nakanishi, Wilhelm Schlag 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2011 215 $a1 online resource (258 pages) 225 0 $aZurich Lectures in Advanced Mathematics (ZLAM) 330 $aThe notion of an invariant manifold arises naturally in the asymptotic stability analysis of stationary or standing wave solutions of unstable dispersive Hamiltonian evolution equations such as the focusing semilinear Klein-Gordon and Schro?dinger equations. This is due to the fact that the linearized operators about such special solutions typically exhibit negative eigenvalues (a single one for the ground state), which lead to exponential instability of the linearized flow and allows for ideas from hyperbolic dynamics to enter. One of the main results proved here for energy subcritical equations is that the center-stable manifold associated with the ground state appears as a hyper-surface which separates a region of finite-time blowup in forward time from one which exhibits global existence and scattering to zero in forward time. Our entire analysis takes place in the energy topology, and the conserved energy can exceed the ground state energy only by a small amount. This monograph is based on recent research by the authors and the proofs rely on an interplay between the variational structure of the ground states on the one hand, and the nonlinear hyperbolic dynamics near these states on the other hand. A key element in the proof is a virial-type argument excluding almost homoclinic orbits originating near the ground states, and returning to them, possibly after a long excursion. These lectures are suitable for graduate students and researchers in partial differential equations and mathematical physics. For the cubic Klein-Gordon equation in three dimensions all details are provided, including the derivation of Strichartz estimates for the free equation and the concentration-compactness argument leading to scattering due to Kenig and Merle. 606 $aDifferential equations$2bicssc 606 $aPartial differential equations$2msc 615 07$aDifferential equations 615 07$aPartial differential equations 686 $a35-xx$2msc 700 $aNakanishi$b Kenji$01071340 702 $aSchlag$b Wilhelm 801 0$bch0018173 906 $aBOOK 912 $a9910151928703321 996 $aInvariant Manifolds and Dispersive Hamiltonian Evolution Equations$92566850 997 $aUNINA LEADER 01465nam 2200457 450 001 9910163134803321 005 20230807213148.0 010 $a3-86496-832-1 035 $a(CKB)3710000001045551 035 $a(MiAaPQ)EBC4418081 035 $a(Au-PeEL)EBL4418081 035 $a(CaPaEBR)ebr11349412 035 $a(OCoLC)974589056 035 $a(EXLCZ)993710000001045551 100 $a20151120h20152015 uy| 0 101 0 $ager 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 14$aDer Fall Hoeness als Skandal in den Medien $eAnschlusskommunikation, Authentisierung und Systemstabilisierung /$fPetja Posor 210 1$aKonstanz :$cUVK Verlagsgesellschaft,$d[2015] 210 4$d©2015 215 $a1 online resource (111 pages) $cillustrations 225 1 $aMedienwissenschaft 300 $aThesis (master's)-Universita?t, Erlangen-Nu?rnberg, 2013. 311 $a3-86764-594-9 320 $aIncludes bibliographical references. 410 0$aMedienwissenschaft (Konstanz, Germany) 606 $aScandals in mass media 606 $aMass media$xObjectivity 615 0$aScandals in mass media. 615 0$aMass media$xObjectivity. 700 $aPosor$b Petja$01247851 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910163134803321 996 $aDer Fall Hoeness als Skandal in den Medien$92892499 997 $aUNINA LEADER 03008nas 2200925-a 450 001 996211404803316 005 20230223213019.0 011 $a1521-0103 035 $a(DE-599)ZDB1475023-5 035 $a(OCoLC)39612107 035 $a(CKB)954925416981 035 $a(CONSER)sn-98001123- 035 $a(EXLCZ)99954925416981 100 $a19980729a19099999 s-- a 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe journal of pharmacology and experimental therapeutics 210 $a[Bethesda, Md.] $cAmerican Society for Pharmacology and Experimental Therapeutics$d[1909]- 300 $aRefereed/Peer-reviewed 300 $aPublished with the assistance of HighWire Press, the Internet imprint of the Stanford University Libraries. 300 $aTitle from issue table of contents screen (publisher's Web site, viewed June 29, 2006). 311 $a0022-3565 517 3 $aPharmacology and experimental therapeutics 517 1 $aJPET online 531 $aJ PHARMACOL EXP THER 531 $aJ PHARM EXP 531 $aJOURNAL OF PHARMACOLOGY & EXPERIMENTAL THERAPEUTICS 531 $aJOURNAL OF PHARMACOLOGY AND EXPERIMENTAL THERAPEUTICS 531 $aJPET 531 $aTHE JOURNAL OF PHARMACOLOGY & EXPERIMENTAL THERAPEUTICS 531 $aJ. PHARMACOL. EXP. 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