FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1904393121> ?p ?o ?g. }

• W1904393121 endingPage "1046" @default.
• W1904393121 startingPage "967" @default.
• W1904393121 abstract "We study highly oscillating solutions to a class of weakly well-posed hyperbolic initial boundary value problems. Weak well-posedness is associated with an amplification phenomenon of oscillating waves on the boundary. In some previous works, we have rigorously justified a {sl weakly nonlinear} regime for {sl semilinear} problems. In that case, the forcing term on the boundary has amplitude $O(varepsilon^2)$ and oscillates at a frequency $O(1/varepsilon)$. The corresponding exact solution, which has been shown to exist on a time interval that is independent of $varepsilon in (0,1]$, has amplitude $O(varepsilon)$. In this paper, we deal with the exact same scaling, namely $O(varepsilon^2)$ forcing term on the boundary and $O(varepsilon)$ solution, for {sl quasilinear} problems. In analogy with the work by Cheverry, Gu`es and M'etivier, this corresponds to a {sl strongly nonlinear} regime, and our main result proves solvability for the corresponding WKB cascade of equations, which yields existence of approximate solutions on a time interval that is independent of $varepsilonin (0,1]$. Existence of exact solutions close to approximate ones is a stability issue which highly depends on the hyperbolic system and on the boundary conditions; we do not address that question here. This work encompasses previous formal expansions by Majda and Rosales in the case of weakly stable shock waves, and by Artola and Majda for two-dimensional compressible vortex sheets. In particular, we prove well-posedness for the leading amplitude equation derived by Majda and Rosales (the ``Mach stem equation'') and generalize its derivation to a large class of hyperbolic boundary value problems and to periodic forcing terms. The latter case is solved under a crucial nonresonant assumption and a small divisor condition." @default.
• W1904393121 created "2016-06-24" @default.
• W1904393121 creator A5038805423 @default.
• W1904393121 creator A5051917893 @default.
• W1904393121 date "2017-01-01" @default.
• W1904393121 modified "2023-10-15" @default.
• W1904393121 title "The Mach stem equation and amplification in strongly nonlinear geometric optics" @default.
• W1904393121 cites W1492628501 @default.
• W1904393121 cites W1494179959 @default.
• W1904393121 cites W1543729115 @default.
• W1904393121 cites W1594106146 @default.
• W1904393121 cites W1616357899 @default.
• W1904393121 cites W1661164962 @default.
• W1904393121 cites W1977082098 @default.
• W1904393121 cites W1983197586 @default.
• W1904393121 cites W1984651586 @default.
• W1904393121 cites W1999118180 @default.
• W1904393121 cites W2001890138 @default.
• W1904393121 cites W2004993859 @default.
• W1904393121 cites W2009297166 @default.
• W1904393121 cites W2010736397 @default.
• W1904393121 cites W2020756646 @default.
• W1904393121 cites W2030437981 @default.
• W1904393121 cites W2041270625 @default.
• W1904393121 cites W2046367157 @default.
• W1904393121 cites W2056057468 @default.
• W1904393121 cites W2061680697 @default.
• W1904393121 cites W2065165310 @default.
• W1904393121 cites W2072332979 @default.
• W1904393121 cites W2084721092 @default.
• W1904393121 cites W210212762 @default.
• W1904393121 cites W2105137108 @default.
• W1904393121 cites W2229872953 @default.
• W1904393121 cites W2234737328 @default.
• W1904393121 cites W2294153152 @default.
• W1904393121 cites W2962695325 @default.
• W1904393121 doi "https://doi.org/10.1353/ajm.2017.0026" @default.
• W1904393121 hasPublicationYear "2017" @default.
• W1904393121 type Work @default.
• W1904393121 sameAs 1904393121 @default.
• W1904393121 citedByCount "7" @default.
• W1904393121 countsByYear W19043931212019 @default.
• W1904393121 countsByYear W19043931212020 @default.
• W1904393121 countsByYear W19043931212021 @default.
• W1904393121 countsByYear W19043931212022 @default.
• W1904393121 crossrefType "journal-article" @default.
• W1904393121 hasAuthorship W1904393121A5038805423 @default.
• W1904393121 hasAuthorship W1904393121A5051917893 @default.
• W1904393121 hasBestOaLocation W19043931212 @default.
• W1904393121 hasConcept C111615704 @default.
• W1904393121 hasConcept C121332964 @default.
• W1904393121 hasConcept C129747778 @default.
• W1904393121 hasConcept C134306372 @default.
• W1904393121 hasConcept C158622935 @default.
• W1904393121 hasConcept C165231844 @default.
• W1904393121 hasConcept C180205008 @default.
• W1904393121 hasConcept C182310444 @default.
• W1904393121 hasConcept C33923547 @default.
• W1904393121 hasConcept C37914503 @default.
• W1904393121 hasConcept C57879066 @default.
• W1904393121 hasConcept C62354387 @default.
• W1904393121 hasConcept C62520636 @default.
• W1904393121 hasConcept C78045399 @default.
• W1904393121 hasConceptScore W1904393121C111615704 @default.
• W1904393121 hasConceptScore W1904393121C121332964 @default.
• W1904393121 hasConceptScore W1904393121C129747778 @default.
• W1904393121 hasConceptScore W1904393121C134306372 @default.
• W1904393121 hasConceptScore W1904393121C158622935 @default.
• W1904393121 hasConceptScore W1904393121C165231844 @default.
• W1904393121 hasConceptScore W1904393121C180205008 @default.
• W1904393121 hasConceptScore W1904393121C182310444 @default.
• W1904393121 hasConceptScore W1904393121C33923547 @default.
• W1904393121 hasConceptScore W1904393121C37914503 @default.
• W1904393121 hasConceptScore W1904393121C57879066 @default.
• W1904393121 hasConceptScore W1904393121C62354387 @default.
• W1904393121 hasConceptScore W1904393121C62520636 @default.
• W1904393121 hasConceptScore W1904393121C78045399 @default.
• W1904393121 hasIssue "4" @default.
• W1904393121 hasLocation W19043931211 @default.
• W1904393121 hasLocation W19043931212 @default.
• W1904393121 hasLocation W19043931213 @default.
• W1904393121 hasLocation W19043931214 @default.
• W1904393121 hasLocation W19043931215 @default.
• W1904393121 hasLocation W19043931216 @default.
• W1904393121 hasOpenAccess W1904393121 @default.
• W1904393121 hasPrimaryLocation W19043931211 @default.
• W1904393121 hasRelatedWork W1810361596 @default.
• W1904393121 hasRelatedWork W2014216602 @default.
• W1904393121 hasRelatedWork W2025089220 @default.
• W1904393121 hasRelatedWork W2106588692 @default.
• W1904393121 hasRelatedWork W2111215486 @default.
• W1904393121 hasRelatedWork W2754383454 @default.
• W1904393121 hasRelatedWork W3025079748 @default.
• W1904393121 hasRelatedWork W4300521771 @default.
• W1904393121 hasRelatedWork W4366373406 @default.
• W1904393121 hasRelatedWork W2560631265 @default.
• W1904393121 hasVolume "139" @default.
• W1904393121 isParatext "false" @default.

• next