Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Meccanica
Erschienen in: Meccanica 15/2017

24.03.2017

Moving boundary problems for an extended Dym equation. Reciprocal connection

verfasst von: Colin Rogers

Erschienen in: Meccanica | Ausgabe 15/2017

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Stefan-type moving boundary problems are investigated for an extended Dym equation originally introduced in work of Camassa and Holm. Reduction is made to an associated class of moving boundary value problems for the canonical integrable Dym equation and exact solution obtained in terms of Yablonski–Vorob’ev polynomials via a Painlevé II reduction.
Vorheriger Artikel Vehicle sideslip angle estimation via a Riccati equation based nonlinear filter
Nächster Artikel Effect of the initial ramps of creep and relaxation tests on models with fractional derivatives

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Fußnoten
1
Hereafter denoted by \(P_{\mathrm {II}}\)
 
Literatur
1.
Rubinstein LI (1971) The Stefan problem, American Mathematical Society Translations, vol 27. American Mathematical Society, Providence
2.
Friedman A (1982) Variational principles and free boundary problems. Wiley, New YorkMATH
3.
Elliot CM, Ockendon JR (1982) Weak and variational methods for moving boundary problems, research notes in mathematics 59. Pitman, New York
4.
Crank J (1984) Free and moving boundary value problems. Clarendon Press, OxfordMATH
5.
Alexides V, Solomon AD (1996) Mathematical modelling of melting and freezing processes. Hemisphere Publishing Corporation, Taylor and Francis, Washington
6.
Tarzia DA (2000) A bibliography on moving-free boundary problems for heat diffusion equation. Stefan Probl Mat Ser A2:1–297
7.
Rogers C, Schief WK (2002) Bäcklund and Darboux transformations. geometry and modern applications in soliton theory, cambridge texts in applied mathematics. Cambridge University Press, CambridgeMATH
8.
9.
Vasconcelos GL, Kadanoff LP (1991) Stationary solutions for the Saffman–Taylor problem with surface tension. Phys Rev A 44:6490–6495ADSCrossRef
10.
Kruskal M (1975) Nonlinear wave equations. In: Moser Jürgen J (ed) Dynamical systems, theory and applications, lecture notes in physics. Springer, Heidelberg, pp 310–354CrossRef
11.
Vassiliou PJ (2001) Harry Dym equation, In: Encyclopaedia of mathematics, Springer
12.
13.
Fokas AS, Tanveer S (1998) A Hele–Shaw problem and the second Painlevé transcendent. Math Proc Camb Phil Soc 124:169–191CrossRefMATH
14.
15.
Schief WK, Rogers C (1999) Binormal motion of curves of constant curvature and torsion. Generation of soliton surfaces. Proc R Soc Lond A 455:3163–3188ADSCrossRefMATHMathSciNet
16.
Da Rios LS (1906) Sul moto d’un liquido indefinito con un filetto vorticoso. Rend Circ Mat Palermo 22:117–135CrossRefMATH
17.
18.
19.
20.
Rogers C, Schief WK (1998) Intrinsic geometry of the NLS equation and its auto-Bäcklund transformation. Stud Appl Math 101:267–287CrossRefMATHMathSciNet
21.
22.
23.
24.
Dai HH, Pavlov M (1998) Transformations for the Camassa–Holm equation, its high frequency limit and the sinh–Gordon equation. J Phys Soc Jpn 67:3655–3657ADSCrossRefMATHMathSciNet
25.
Lukashevich NA (1971) The second Painlevé equation. Diff Eq 7:853–854MATH
26.
Gromak VI (1999) Bäcklund transformations of Painlevé equations and their applications. In: Conte R (ed) The Painlevë property: one century later. Springer-Verlag, New York, pp 687–734CrossRef
27.
Yablonskii AI (1959) On rational solutions of the second Painlevé equation. Vesti Akad Nauk B55R ser Fiz Tkh Nauk 3:30–35
28.
Vorob’ev AP (1965) On the rational solutions of the second Painlevé equation. Diff Eq 1:79–81MATH
29.
Rogers C, Bassom A, Schief WK (1999) On a Painlevé model in steady electrolysis: application of a Bäcklund transformation. J Math Anal Appl 240:367–381CrossRefMATHMathSciNet
30.
Bass LK, Nimmo J, Rogers C, Schief WK (2010) Electrical structures of interfaces. A Painlevé II model. Proc R Soc Lond A 466:2117–2136ADSCrossRefMATHMathSciNet
31.
Bracken AJ, Bass LK, Rogers C (2012) Bäcklund flux-quantization in a model of electrodiffusion based on Painlevé II. J Phys A Math Theor 45:105204ADSCrossRefMATH
32.
33.
Rogers C (1968) Reciprocal relations in non-steady one-dimensional gasdynamics. Zeit Angew Math Phys 19:58–63CrossRefMATH
34.
Rogers C (1969) Invariant transformations in non-steady gasdynamics and magneto-gasdynamics. Zeit Angew Math Phys 20:370–382CrossRefMATH
35.
Rogers C, Wong P (1984) On reciprocal Bäcklund transformations of inverse scattering schemes. Phys Scr 30:10–14ADSCrossRefMATH
36.
Rogers C (1987) The Harry Dym equation in 2+1-dimensions: a reciprocal link with the Kadomtsev-Petviashvili equation. Phys Lett 120A:15–18ADSCrossRefMathSciNet
37.
38.
Hereman W, Banerjee PP, Chatterjee MR (1989) Derivation and explicit solution of the Harry Dym equation and its connections with the Korteweg-de-Vries equation. J Phys A 22:241–255ADSCrossRefMATHMathSciNet
39.
Rogers C, Carillo S (1987) On reciprocal properties of the Caudrey–Dodd–Gibbon and Kaup–Kuperschmidt hierarchies. Phys Scr 36:865–869ADSCrossRefMATH
40.
41.
Konopelchenko B, Rogers C (1992) Bäcklund and reciprocal transformations: gauge connections. In: Ames WF, Rogers C (eds) Nonlinear equations in applied science. Academic Press, New York, pp 317–362CrossRef
42.
43.
Donato A, Ramgulam U, Rogers C (1992) The 3+1-dimensional Monge-Ampère equation in discontinuity wave theory: application of a reciprocal transformation. Meccanica 27:257–262CrossRefMATH
44.
Rogers C, Shadwick WE (1982) Bäcklund transformations and their applications. Academic Press, New YorkMATH
45.
Rogers C, Kingston JG, Shadwick WF (1980) On reciprocal-type invariant transformations in magnetogasdynamics. J Math Phys 21:395–397ADSCrossRefMATH
46.
47.
Rogers C (1986) On a class of moving boundary problems in nonlinear heat conduction. Application of a Bäcklund transformation. Int J Nonlinear Mech 21:249–256CrossRefMATH
48.
49.
Rogers C, Guo BY (1988) A note on the onset of melting in a class of simple metals. Conditions on the applied boundary flux. Acta Math Sci 8:425–430MATHMathSciNet
50.
Tarzia DA (1981) An inequality for the coefficient \(\sigma\) of the free boundary \(s(t)=\sigma \sqrt{t}\) of the Neumann problem for the two-phase Stefan problem. Quart Appl Math 39:491–497CrossRefMathSciNet
51.
52.
Fokas AS, Rogers C, Schief WK (2005) Evolution of methacrylate distribution during wood saturation. A nonlinear moving boundary problem. Appl Math Lett 18:321–328CrossRefMATHMathSciNet
53.
54.
55.
Rogers C, Nucci MC (1986) On reciprocal Bäcklund transformations and the Korteweg-de Vries hierarchy. Phys Scr 33:289–292ADSCrossRefMATH
56.
Rogers C (2015) Moving boundary problems for the Harry Dym equation and its reciprocal associates. Z Angew Math Phys 66:3025–3220MATHMathSciNet
Metadaten
Titel
Moving boundary problems for an extended Dym equation. Reciprocal connection
verfasst von
Colin Rogers
Publikationsdatum
24.03.2017
Verlag
Springer Netherlands
Erschienen in
Meccanica / Ausgabe 15/2017
Print ISSN: 0025-6455
Elektronische ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-017-0662-9

Weitere Artikel der Ausgabe 15/2017

Meccanica 15/2017 Zur Ausgabe

OriginalPaper

Effect of the initial ramps of creep and relaxation tests on models with fractional derivatives

OriginalPaper

Numerical calculation of air entrainment rates due to intake vortices

OriginalPaper

Vehicle sideslip angle estimation via a Riccati equation based nonlinear filter

OriginalPaper

Duty cycle and directional jet effects of a plasma actuator on the flow control around a NACA0015 airfoil

OriginalPaper

Non-isothermal flow of a Bingham fluid with pressure and temperature dependent viscosity

OriginalPaper

CFD investigation on mixing in a rapidly mixed tubular flame burner

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise