Analysis and numerical approximation of singular boundary value problems with the p-Laplacian in fluid mechanics

This paper studies a generalization of the Cahn–Hilliard continuum model for multi-phase fluids where the classical Laplacian has been replaced by a degenerate one (i.e., the so-called p-Laplacian). The solution’s asymptotic behavior is analyzed at two singular points; namely, at the origin and at i...

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Veröffentlicht in:Journal of computational and applied mathematics Jg. 262; S. 87 - 104
Hauptverfasser: Kulikov, G.Yu, Lima, P.M., Morgado, M.L.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 15.05.2014
Schlagworte:
Degenerate Laplacian
Nested implicit Runge–Kutta formulas with global error control
Nonlinear ordinary differential equations
Shooting method
Singular boundary value problems
65L05
34B16
Degenerate Laplacian
Nonlinear ordinary differential equations
Nested implicit Runge–Kutta formulas with global error control
Singular boundary value problems
Shooting method
ISSN:0377-0427, 1879-1778
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:This paper studies a generalization of the Cahn–Hilliard continuum model for multi-phase fluids where the classical Laplacian has been replaced by a degenerate one (i.e., the so-called p-Laplacian). The solution’s asymptotic behavior is analyzed at two singular points; namely, at the origin and at infinity. An efficient technique for treating such singular boundary value problems is presented, and results of numerical integration are discussed and compared with earlier computed data.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2013.09.071