LEADER 04935nam 22006613 450 001 9910960017603321 005 20231110223118.0 010 $a9781470471699 010 $a1470471698 035 $a(MiAaPQ)EBC29379018 035 $a(Au-PeEL)EBL29379018 035 $a(CKB)24267685500041 035 $a(OCoLC)1336954728 035 $a(EXLCZ)9924267685500041 100 $a20220721d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aType II Blow up Solutions with Optimal Stability Properties for the Critical Focussing Nonlinear Wave Equation on 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2022. 210 4$dİ2022. 215 $a1 online resource (88 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.278 311 08$aPrint version: Burzio, Stefano Type II Blow up Solutions with Optimal Stability Properties for the Critical Focussing Nonlinear Wave Equation on Providence : American Mathematical Society,c2022 9781470453466 327 $aCover -- Title page -- Chapter 1. Introduction -- 1.1. The type II blow up solutions of [33], [32] -- 1.2. The effect of symmetries on the solutions of Theorem 1.1 -- 1.3. Conditional stability of type II solutions -- 1.4. Spectral theory associated with the linearisation ? -- 1.5. Description of the data perturbation in terms of the distorted Fourier transform -- 1.6. Outline of the main result from [26] -- 1.7. Figures -- Chapter 2. The main theorem and outline of the proof -- 2.1. The main theorem -- 2.2. Outline of the proof -- Chapter 3. Construction of a two parameter family of approximate blow up solutions -- 3.1. Step 0: the bulk term -- 3.2. Step 1: choice of the first correction ? -- 3.3. Step 2: the ? error -- 3.4. Step 3: choice of second correction ? -- 3.5. Step 4: the ? error -- 3.6. Step 5: inductive step -- 3.7. Step 6: choice of _{ ?, }, =1,2 -- Chapter 4. Modulation theory -- determination of the parameters _{1,2}. -- 4.1. Re-scalings and the distorted Fourier transform -- 4.2. The effect of scaling the bulk part -- Chapter 5. Iterative construction of blow up solution almost matching the perturbed initial data -- 5.1. Formulation of the perturbation problem on Fourier side -- 5.2. The proof of Theorem 5.1 -- 5.3. Translation to original coordinate system -- Chapter 6. Proof of Theorem 2.1 -- Chapter 7. Outlook -- Bibliography -- Index -- Back Cover. 330 $a"We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation on constructed in Krieger, Schlag, and Tartaru ("Slow blow-up solutions for the critical focusing semilinear wave equation", 2009) and Krieger and Schlag ("Full range of blow up exponents for the quintic wave equation in three dimensions", 2014) are stable along a co-dimension one Lipschitz manifold of data perturbations in a suitable topology, provided the scaling parameter is sufficiently close to the self-similar rate, i. e., is sufficiently small. This result is qualitatively optimal in light of the result of Krieger, Nakamishi, and Schlag ("Center-stable manifold of the ground state in the energy space for the critical wave equation", 2015). The paper builds on the analysis of Krieger and Wong ("On type I blow-up formation for the critical NLW", 2014)"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aNonlinear wave equations 606 $aBlowing up (Algebraic geometry) 606 $aPerturbation (Mathematics) 606 $aAsymptotic expansions 606 $aIterative methods (Mathematics) 606 $aFourier transformations 606 $aPartial differential equations -- Hyperbolic equations and systems -- Wave equation$2msc 606 $aPartial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutions$2msc 615 0$aNonlinear wave equations. 615 0$aBlowing up (Algebraic geometry) 615 0$aPerturbation (Mathematics) 615 0$aAsymptotic expansions. 615 0$aIterative methods (Mathematics) 615 0$aFourier transformations. 615 7$aPartial differential equations -- Hyperbolic equations and systems -- Wave equation. 615 7$aPartial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutions. 676 $a515/.353 676 $a515.353 686 $a35L05$a35B40$2msc 700 $aBurzio$b Stefano$01800729 701 $aKrieger$b Joachim$01071019 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910960017603321 996 $aType II Blow up Solutions with Optimal Stability Properties for the Critical Focussing Nonlinear Wave Equation on$94345650 997 $aUNINA LEADER 02897nam 22007575 450 001 9910132294503321 005 20250609111909.0 010 $a9781137500281 010 $a113750028X 024 7 $a10.1057/9781137500281 035 $a(CKB)3710000000336250 035 $a(SSID)ssj0001468419 035 $a(PQKBManifestationID)11902734 035 $a(PQKBTitleCode)TC0001468419 035 $a(PQKBWorkID)11527329 035 $a(PQKB)10573385 035 $a(DE-He213)978-1-137-50028-1 035 $a(MiAaPQ)EBC1863941 035 $a(MiAaPQ)EBC6422620 035 $a(Au-PeEL)EBL6422620 035 $a(OCoLC)894334805 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/34952 035 $a(PPN)192218204 035 $a(ScCtBLL)a85e38ba-0acd-46c1-ba5c-e687bcd0b242 035 $a(Perlego)4572438 035 $a(Perlego)2338778 035 $a(MiAaPQ)EBC4390030 035 $a(oapen)doab34952 035 $a(EXLCZ)993710000000336250 100 $a20151218d2015 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHumanities World Report 2015 /$fby P. Holm, A. Jarrick, D. Scott 205 $a1st ed. 2015. 210 $aBasingstoke$cSpringer Nature$d2015 210 1$aLondon :$cPalgrave Macmillan UK :$cImprint: Palgrave Macmillan,$d2015. 215 $a1 online resource (ix 215 pages) $cdigital, PDF file(s) 300 $aEBL Purchase. 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$aPrint version: 9781137500274 320 $aIncludes bibliographical references and index. 330 $aThis book is open access under a CC BY license. The first of its kind, this Open Access 'Report' is a first step in assessing the state of the humanities worldwide. Based on an extensive literature review and enlightening interviews the book discusses the value of the humanities, the nature of humanities research and the relation between humanities and politics, amongst other issues. 606 $aLiterature$xPhilosophy 606 $aCulture$xStudy and teaching 606 $aSocial policy 606 $aLiterary Theory 606 $aCultural Theory 606 $aSocial Policy 615 0$aLiterature$xPhilosophy. 615 0$aCulture$xStudy and teaching. 615 0$aSocial policy. 615 14$aLiterary Theory. 615 24$aCultural Theory. 615 24$aSocial Policy. 676 $a801 700 $aHolm$b Poul$4aut$4http://id.loc.gov/vocabulary/relators/aut$01791486 702 $aJarrick$b Arne$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aScott$b Dominic$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bUkMaJRU 906 $aBOOK 912 $a9910132294503321 996 $aHumanities World Report 2015$94328835 997 $aUNINA