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The nonlinear steepest descent method: Asymptotics for initial-boundary value problems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6191-7769
2016 (English)In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 48, no 3, 2076-2118 p.Article in journal (Refereed) Published
Abstract [en]

We consider the rigorous derivation of asymptotic formulas for initial-boundary value problems using the nonlinear steepest descent method. We give detailed derivations of the asymptotics in the similarity and self-similar sectors for the modified Korteweg-de Vries equation in the quarter-plane. Precise and uniform error estimates are presented in detail.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics Publications , 2016. Vol. 48, no 3, 2076-2118 p.
Keyword [en]
Asymptotic analysis, Initial-boundary value problem, Long time asymptotics, Nonlinear steepest descent, Riemann-Hilbert problem
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-195391DOI: 10.1137/15M1036889ISI: 000385019900017ScopusID: 2-s2.0-84977274755OAI: oai:DiVA.org:kth-195391DiVA: diva2:1044430
Funder
Swedish Research Council, 2015-05430
Note

QC 20161103

Available from: 2016-11-03 Created: 2016-11-03 Last updated: 2016-11-11Bibliographically approved

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Lenells, Jonatan
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