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245 10 a| Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on R3+1h| [electronic resource] /c| Stefano Burzio, Joachim Krieger.;

260 a| Providence, RI :b| American Mathematical Society,c| [2022];

300 a| iii, 75 pagesb| illustrationsc| 26 cm;

334 a| single unitb| mono0| http://id.loc.gov/vocabulary/issuance/mono;

353 a| bibliographyb| bibliography0| http://id.loc.gov/vocabulary/msupplcont/bibliography;

353 a| indexb| index0| http://id.loc.gov/vocabulary/msupplcont/index;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| number 1369;

500 a| "July 2022, volume 278, number 1369 (fourth of 6 numbers).";

504 a| Includes bibliographical references and index.;

505 0 a| The main theorem and outline of the proof -- Construction of a two parameter family of approximate blow up solutions -- Modulation theory; determination of the parameters [gamma]1,2. -- Iterative construction of blow up solution almost matching the perturbed initial data -- Proof of theorem 2.1 -- Outlook.;

506 a| Available only to authorized users.;

520 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)"-- Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Nonlinear wave equations0| http://id.loc.gov/authorities/subjects/sh89005869=| ^A386707;

650 0 a| Blowing up (Algebraic geometry)0| http://id.loc.gov/authorities/subjects/sh88000905=| ^A491068;

650 0 a| Perturbation (Mathematics)0| http://id.loc.gov/authorities/subjects/sh85100181=| ^A37881;

650 0 a| Asymptotic expansions0| http://id.loc.gov/authorities/subjects/sh85009056=| ^A56509;

650 0 a| Iterative methods (Mathematics)0| http://id.loc.gov/authorities/subjects/sh85069058=| ^A19810;

650 0 a| Fourier transformations0| http://id.loc.gov/authorities/subjects/sh85051094=| ^A23965;

650 7 a| Partial differential equations -- Hyperbolic equations and systems -- Wave equation2| msc;

650 7 a| Partial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutions2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Krieger, Joachim,d| 19761| http://id.loc.gov/rwo/agents/no2003053557.?| UNAUTHORIZED;

758 1| http://id.loc.gov/resources/instances/22751732;

758 4| http://id.loc.gov/ontologies/bibframe/instanceOf1| http://id.loc.gov/resources/works/22751732;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=29379018;

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Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on R3+1 / Stefano Burzio, Joachim Krieger.

Author/creator	Burzio, Stefano, 1989
Other author	Krieger, Joachim, 1976
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, [2022]
Description	iii, 75 pages illustrations 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Nonlinear wave equations Blowing up (Algebraic geometry) Perturbation (Mathematics) Asymptotic expansions Iterative methods (Mathematics) Fourier transformations

Series	Memoirs of the American Mathematical Society, 0065-9266 ; number 1369
Contents	The main theorem and outline of the proof -- Construction of a two parameter family of approximate blow up solutions -- Modulation theory; determination of the parameters [gamma]1,2. -- Iterative construction of blow up solution almost matching the perturbed initial data -- Proof of theorem 2.1 -- Outlook.
Abstract	"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)"-- Provided by publisher.
General note	"July 2022, volume 278, number 1369 (fourth of 6 numbers)."
Bibliography note	Includes bibliographical references and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022027945
ISBN	9781470453466 paperback
ISBN	pdf

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Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on R3+1 / Stefano Burzio, Joachim Krieger.

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