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studies a generalization of the Cahn–Hilliard continuum model for multi-phase fluids where the classical Laplacian has been replaced by a degenerate one (i.e., the so-called p-Laplacian).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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| Vydané v: | Journal of computational and applied mathematics Ročník 262; s. 87 - 104 |
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| Jazyk: | English |
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Elsevier B.V
15.05.2014
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| ISSN: | 0377-0427, 1879-1778 |
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| Abstract | 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studies a generalization of the Cahn–Hilliard continuum model for multi-phase fluids where the classical Laplacian has been replaced by a degenerate one (i.e., the so-called p-Laplacian).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. |
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| AbstractList | 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studies a generalization of the Cahn–Hilliard continuum model for multi-phase fluids where the classical Laplacian has been replaced by a degenerate one (i.e., the so-called p-Laplacian).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. |
| Author | Lima, P.M. Kulikov, G.Yu Morgado, M.L. |
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| Cites_doi | 10.1515/rnam.2007.029 10.1007/s10915-007-9141-0 10.1063/1.1744102 10.1090/conm/540/10662 10.1016/j.cam.2005.05.004 10.1016/j.apnum.2008.03.019 10.1093/imanum/drr060 10.1137/S0036141003437678 10.1142/S0218202596000341 10.1016/j.na.2009.10.011 10.1137/0713063 10.1090/S0025-5718-1979-0521281-7 10.4171/JEMS/31 10.1137/0908047 10.1016/S0041-5553(83)80104-9 10.1134/S0965542508110109 10.1016/0020-7225(95)00141-7 10.1016/j.mcm.2009.10.042 |
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| Keywords | 65L05 34B16 Degenerate Laplacian Nonlinear ordinary differential equations Nested implicit Runge–Kutta formulas with global error control Singular boundary value problems Shooting method |
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| References | Ascher, Bader (br000085) 1987; 8 Savin, Valdinoci, Sciunzi (br000060) 2006; 182 G. Hastermann, P.M. Lima, M.L. Morgado, E.B. Weinmüller, Density profile equation with Takac (br000075) 2009; 17 Dell’Isola, Gouin, Seppecher (br000155) 1995; 320 Kierzienka, Shampine (br000095) 2008; 3 Ascher, Christiansen, Russel (br000080) 1978; 33 Linde (br000160) 1990 Sciunzi, Valdinoci (br000050) 2005; 7 Dell’Isola, Gouin, Rotoli (br000150) 1996; 15 Lima, Konyukhova, Chemetov, Sukov (br000030) 2006; 189 Cahn, Hilliard (br000010) 1958; 28 Petrosyan, Valdinoci (br000055) 2005; 36 Shampine, Muir, Xu (br000100) 2006; 1 Kulikov (br000140) 2013; 33 Rachunkova, Rachunek, Tomecek (br000045) 2011; 2011 Laplacian: analysis and numerical simulation, Appl. Math. Comput. (to appear). Seppecher (br000005) 1996; 34 Gurtin, Polignone, Vinals (br000015) 1996; 6 Drabek, Manasevich, Takac (br000070) 2011; 540 2000. Available at de Hoog, Weiss (br000105) 1976; 13 Lyapunov (br000130) 1947; vol. 17 Kulikov, Shindin (br000135) 2009; 59 L. Shampine, J. Kierzienka, M. Reichelt, Solving boundary value problems for ordinary differential equations in MATLAB with Konyukhova, Lima, Morgado, Soloviev (br000025) 2008; 48 . Rachunkova, Tomecek (br000035) 2010; 72 Rachunkova, Tomecek (br000040) 2010; 51 Kulikov, Merkulov, Shindin (br000145) 2007; 22 W. Kitzhofer, G. Pulverer, O. Koch, C. Simon, E.B. Weinmüller, BVPSUITE, A new MATLAB code for singular implicit boundary value problems, 2009. Available at Kitzhofer, Koch, Pulverer, Simon, Weinmüller (br000120) 2010; 5 W. Auzinger, G. Kneisl, O. Koch, E.B. Weinmüller, Manual and Code: SBVP, A MATLAB solver for singular boundary value problems, 2003. Available at Kitzhofer, Koch, Lima, Weinmüller (br000020) 2007; 32 Konyukhova (br000125) 1983; 23 Kulikov (10.1016/j.cam.2013.09.071_br000145) 2007; 22 Seppecher (10.1016/j.cam.2013.09.071_br000005) 1996; 34 10.1016/j.cam.2013.09.071_br000065 Sciunzi (10.1016/j.cam.2013.09.071_br000050) 2005; 7 Konyukhova (10.1016/j.cam.2013.09.071_br000025) 2008; 48 Kierzienka (10.1016/j.cam.2013.09.071_br000095) 2008; 3 Rachunkova (10.1016/j.cam.2013.09.071_br000040) 2010; 51 Cahn (10.1016/j.cam.2013.09.071_br000010) 1958; 28 Ascher (10.1016/j.cam.2013.09.071_br000085) 1987; 8 Shampine (10.1016/j.cam.2013.09.071_br000100) 2006; 1 Takac (10.1016/j.cam.2013.09.071_br000075) 2009; 17 Dell’Isola (10.1016/j.cam.2013.09.071_br000155) 1995; 320 10.1016/j.cam.2013.09.071_br000115 Kulikov (10.1016/j.cam.2013.09.071_br000140) 2013; 33 de Hoog (10.1016/j.cam.2013.09.071_br000105) 1976; 13 Savin (10.1016/j.cam.2013.09.071_br000060) 2006; 182 Rachunkova (10.1016/j.cam.2013.09.071_br000045) 2011; 2011 10.1016/j.cam.2013.09.071_br000110 Kulikov (10.1016/j.cam.2013.09.071_br000135) 2009; 59 Dell’Isola (10.1016/j.cam.2013.09.071_br000150) 1996; 15 Linde (10.1016/j.cam.2013.09.071_br000160) 1990 Drabek (10.1016/j.cam.2013.09.071_br000070) 2011; 540 Petrosyan (10.1016/j.cam.2013.09.071_br000055) 2005; 36 Ascher (10.1016/j.cam.2013.09.071_br000080) 1978; 33 10.1016/j.cam.2013.09.071_br000090 Kitzhofer (10.1016/j.cam.2013.09.071_br000120) 2010; 5 Lima (10.1016/j.cam.2013.09.071_br000030) 2006; 189 Kitzhofer (10.1016/j.cam.2013.09.071_br000020) 2007; 32 Gurtin (10.1016/j.cam.2013.09.071_br000015) 1996; 6 Konyukhova (10.1016/j.cam.2013.09.071_br000125) 1983; 23 Lyapunov (10.1016/j.cam.2013.09.071_br000130) 1947; vol. 17 Rachunkova (10.1016/j.cam.2013.09.071_br000035) 2010; 72 |
| References_xml | – reference: W. Kitzhofer, G. Pulverer, O. Koch, C. Simon, E.B. Weinmüller, BVPSUITE, A new MATLAB code for singular implicit boundary value problems, 2009. Available at – volume: 48 start-page: 2018 year: 2008 end-page: 2058 ident: br000025 article-title: Bubbles and droplets in nonlinear physics models: analysis and numerical simulation of singular nonlinear boundary value problems publication-title: Comp. Maths. Math. Phys. – volume: 540 start-page: 95 year: 2011 end-page: 134 ident: br000070 article-title: Manifolds of critical points in a quasi-linear model for phase transitions publication-title: Contemp. Math. – volume: 22 start-page: 567 year: 2007 end-page: 590 ident: br000145 article-title: Asymptotic error estimate for general Newton-type methods and its application to differential equations publication-title: Russian J. Numer. Anal. Math. Modelling – reference: , 2000. Available at – volume: 28 start-page: 258 year: 1958 end-page: 267 ident: br000010 article-title: Free energy of a nonuniform system. I. Interfacial free energy publication-title: J. Chem. Phys. – volume: vol. 17 year: 1947 ident: br000130 publication-title: Probleme General de la Stabilite du Mouvement – volume: 2011 year: 2011 ident: br000045 article-title: Existence of oscillatory solutions of singular nonlinear differential equations publication-title: Abstr. Appl. Anal. – volume: 8 start-page: 483 year: 1987 end-page: 500 ident: br000085 article-title: A new implementation for a mixed order boundary value ODE solver publication-title: SIAM J. Sci. Stat. Comput. – reference: -Laplacian: analysis and numerical simulation, Appl. Math. Comput. (to appear). – volume: 72 start-page: 2114 year: 2010 end-page: 2118 ident: br000035 article-title: Strictly increasing solutions of a nonlinear singular differential equation arising in hydrodynamics publication-title: Nonlinear Anal. – volume: 7 start-page: 319 year: 2005 end-page: 359 ident: br000050 article-title: Mean curvature properties for publication-title: J. Eur. Math. Soc. – volume: 182 year: 2006 ident: br000060 article-title: Flat level set of publication-title: Mem. Amer. Math. Soc. – volume: 5 start-page: 113 year: 2010 end-page: 134 ident: br000120 article-title: The new MATLAB code BVPSUITE for the solution of singular implicit boundary value problems publication-title: J. Numer. Anal. Inal. Indust. Appl. Math. – volume: 1 start-page: 201 year: 2006 end-page: 217 ident: br000100 article-title: A user-friendly FORTRAN BVP solver publication-title: J. Numer. Anal. Indust. Appl. Math. – volume: 51 start-page: 658 year: 2010 end-page: 669 ident: br000040 article-title: Bubble-type solutions of nonlinear singular problems publication-title: Math. Comput. Modelling – volume: 17 start-page: 227 year: 2009 end-page: 254 ident: br000075 article-title: Stationary radial solutions for a quasilinear Cahn–Hilliard model in publication-title: Electron. J. Differential Equations, Conf. – volume: 32 start-page: 411 year: 2007 end-page: 424 ident: br000020 article-title: Efficient numerical solution of the density profile equation in hydrodynamics publication-title: J. Sci. Comput. – volume: 189 start-page: 260 year: 2006 end-page: 273 ident: br000030 article-title: Analytical-numerical investigation of bubble-type solutions of nonlinear singular problems publication-title: J. Comput. Appl. Math. – volume: 6 start-page: 815 year: 1996 end-page: 831 ident: br000015 article-title: Two-phase binary fluids and immiscible fluids described by an order parameter publication-title: Math. Models Methods Appl. Sci. – volume: 33 start-page: 136 year: 2013 end-page: 163 ident: br000140 article-title: Cheap global error estimation in some Runge–Kutta pairs publication-title: IMA J. Numer. Anal. – volume: 36 start-page: 1057 year: 2005 end-page: 1079 ident: br000055 article-title: Density estimates for a degenerate/singular phase-transition model publication-title: SIAM J. Math. Anal. – volume: 13 start-page: 775 year: 1976 end-page: 813 ident: br000105 article-title: Difference methods for BVPs with a singularity of the second kind publication-title: SIAM J. Numer. Anal. – reference: G. Hastermann, P.M. Lima, M.L. Morgado, E.B. Weinmüller, Density profile equation with – volume: 3 start-page: 27 year: 2008 end-page: 41 ident: br000095 article-title: A BVP solver that controls residual and error publication-title: J. Numer. Anal. Indust. Appl. Math. – reference: . – volume: 15 start-page: 545 year: 1996 end-page: 568 ident: br000150 article-title: Nucleation and shell-like interfaces by second-gradient theory: numerical simulations publication-title: Eur. J. Mech. B/Fluids – volume: 34 start-page: 977 year: 1996 end-page: 992 ident: br000005 article-title: Moving contact lines in the Cahn–Hilliard theory publication-title: Internat. J. Engrg. Sci. – volume: 23 start-page: 72 year: 1983 end-page: 82 ident: br000125 article-title: Singular Cauchy problems for systems of ordinary differential equations publication-title: USSR Comput. Maths. Math. Phys. – volume: 59 start-page: 707 year: 2009 end-page: 722 ident: br000135 article-title: Adaptive nested implicit Runge–Kutta formulas of Gauss type publication-title: Appl. Numer. Math. – reference: L. Shampine, J. Kierzienka, M. Reichelt, Solving boundary value problems for ordinary differential equations in MATLAB with – volume: 33 start-page: 659 year: 1978 end-page: 679 ident: br000080 article-title: A collocation solver for mixed order systems of boundary value problems publication-title: Math. Comp. – volume: 320 start-page: 211 year: 1995 end-page: 216 ident: br000155 article-title: Radius and surface tension of microscopic bubbles second-gradient theory publication-title: C.R. Acad. Sci. Paris – reference: W. Auzinger, G. Kneisl, O. Koch, E.B. Weinmüller, Manual and Code: SBVP, A MATLAB solver for singular boundary value problems, 2003. Available at – year: 1990 ident: br000160 article-title: Particle Physics and Inflationary Cosmology – volume: 182 issue: 858 year: 2006 ident: 10.1016/j.cam.2013.09.071_br000060 article-title: Flat level set of p-Laplace phase transitions publication-title: Mem. Amer. Math. Soc. – volume: 22 start-page: 567 year: 2007 ident: 10.1016/j.cam.2013.09.071_br000145 article-title: Asymptotic error estimate for general Newton-type methods and its application to differential equations publication-title: Russian J. Numer. Anal. Math. Modelling doi: 10.1515/rnam.2007.029 – volume: 5 start-page: 113 year: 2010 ident: 10.1016/j.cam.2013.09.071_br000120 article-title: The new MATLAB code BVPSUITE for the solution of singular implicit boundary value problems publication-title: J. Numer. Anal. Inal. Indust. Appl. Math. – volume: 32 start-page: 411 year: 2007 ident: 10.1016/j.cam.2013.09.071_br000020 article-title: Efficient numerical solution of the density profile equation in hydrodynamics publication-title: J. Sci. Comput. doi: 10.1007/s10915-007-9141-0 – volume: 28 start-page: 258 year: 1958 ident: 10.1016/j.cam.2013.09.071_br000010 article-title: Free energy of a nonuniform system. I. Interfacial free energy publication-title: J. Chem. Phys. doi: 10.1063/1.1744102 – volume: 540 start-page: 95 year: 2011 ident: 10.1016/j.cam.2013.09.071_br000070 article-title: Manifolds of critical points in a quasi-linear model for phase transitions publication-title: Contemp. Math. doi: 10.1090/conm/540/10662 – volume: 17 start-page: 227 year: 2009 ident: 10.1016/j.cam.2013.09.071_br000075 article-title: Stationary radial solutions for a quasilinear Cahn–Hilliard model in N space dimensions publication-title: Electron. J. Differential Equations, Conf. – volume: 1 start-page: 201 year: 2006 ident: 10.1016/j.cam.2013.09.071_br000100 article-title: A user-friendly FORTRAN BVP solver publication-title: J. Numer. Anal. Indust. Appl. Math. – volume: 189 start-page: 260 year: 2006 ident: 10.1016/j.cam.2013.09.071_br000030 article-title: Analytical-numerical investigation of bubble-type solutions of nonlinear singular problems publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2005.05.004 – year: 1990 ident: 10.1016/j.cam.2013.09.071_br000160 – volume: 2011 year: 2011 ident: 10.1016/j.cam.2013.09.071_br000045 article-title: Existence of oscillatory solutions of singular nonlinear differential equations publication-title: Abstr. Appl. Anal. – volume: 3 start-page: 27 year: 2008 ident: 10.1016/j.cam.2013.09.071_br000095 article-title: A BVP solver that controls residual and error publication-title: J. Numer. Anal. Indust. Appl. Math. – volume: vol. 17 year: 1947 ident: 10.1016/j.cam.2013.09.071_br000130 – volume: 59 start-page: 707 year: 2009 ident: 10.1016/j.cam.2013.09.071_br000135 article-title: Adaptive nested implicit Runge–Kutta formulas of Gauss type publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2008.03.019 – volume: 33 start-page: 136 year: 2013 ident: 10.1016/j.cam.2013.09.071_br000140 article-title: Cheap global error estimation in some Runge–Kutta pairs publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drr060 – ident: 10.1016/j.cam.2013.09.071_br000110 – volume: 36 start-page: 1057 year: 2005 ident: 10.1016/j.cam.2013.09.071_br000055 article-title: Density estimates for a degenerate/singular phase-transition model publication-title: SIAM J. Math. Anal. doi: 10.1137/S0036141003437678 – ident: 10.1016/j.cam.2013.09.071_br000115 – volume: 6 start-page: 815 year: 1996 ident: 10.1016/j.cam.2013.09.071_br000015 article-title: Two-phase binary fluids and immiscible fluids described by an order parameter publication-title: Math. Models Methods Appl. Sci. doi: 10.1142/S0218202596000341 – volume: 72 start-page: 2114 year: 2010 ident: 10.1016/j.cam.2013.09.071_br000035 article-title: Strictly increasing solutions of a nonlinear singular differential equation arising in hydrodynamics publication-title: Nonlinear Anal. doi: 10.1016/j.na.2009.10.011 – volume: 320 start-page: 211 year: 1995 ident: 10.1016/j.cam.2013.09.071_br000155 article-title: Radius and surface tension of microscopic bubbles second-gradient theory publication-title: C.R. Acad. Sci. Paris – volume: 13 start-page: 775 year: 1976 ident: 10.1016/j.cam.2013.09.071_br000105 article-title: Difference methods for BVPs with a singularity of the second kind publication-title: SIAM J. Numer. Anal. doi: 10.1137/0713063 – volume: 33 start-page: 659 year: 1978 ident: 10.1016/j.cam.2013.09.071_br000080 article-title: A collocation solver for mixed order systems of boundary value problems publication-title: Math. Comp. doi: 10.1090/S0025-5718-1979-0521281-7 – volume: 7 start-page: 319 year: 2005 ident: 10.1016/j.cam.2013.09.071_br000050 article-title: Mean curvature properties for p-Laplace phase transitions publication-title: J. Eur. Math. Soc. doi: 10.4171/JEMS/31 – volume: 8 start-page: 483 year: 1987 ident: 10.1016/j.cam.2013.09.071_br000085 article-title: A new implementation for a mixed order boundary value ODE solver publication-title: SIAM J. Sci. Stat. Comput. doi: 10.1137/0908047 – ident: 10.1016/j.cam.2013.09.071_br000065 – ident: 10.1016/j.cam.2013.09.071_br000090 – volume: 23 start-page: 72 year: 1983 ident: 10.1016/j.cam.2013.09.071_br000125 article-title: Singular Cauchy problems for systems of ordinary differential equations publication-title: USSR Comput. Maths. Math. Phys. doi: 10.1016/S0041-5553(83)80104-9 – volume: 15 start-page: 545 year: 1996 ident: 10.1016/j.cam.2013.09.071_br000150 article-title: Nucleation and shell-like interfaces by second-gradient theory: numerical simulations publication-title: Eur. J. Mech. B/Fluids – volume: 48 start-page: 2018 year: 2008 ident: 10.1016/j.cam.2013.09.071_br000025 article-title: Bubbles and droplets in nonlinear physics models: analysis and numerical simulation of singular nonlinear boundary value problems publication-title: Comp. Maths. Math. Phys. doi: 10.1134/S0965542508110109 – volume: 34 start-page: 977 year: 1996 ident: 10.1016/j.cam.2013.09.071_br000005 article-title: Moving contact lines in the Cahn–Hilliard theory publication-title: Internat. J. Engrg. Sci. doi: 10.1016/0020-7225(95)00141-7 – volume: 51 start-page: 658 year: 2010 ident: 10.1016/j.cam.2013.09.071_br000040 article-title: Bubble-type solutions of nonlinear singular problems publication-title: Math. Comput. Modelling doi: 10.1016/j.mcm.2009.10.042 |
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| SubjectTerms | Degenerate Laplacian Nested implicit Runge–Kutta formulas with global error control Nonlinear ordinary differential equations Shooting method Singular boundary value problems |
| Title | Analysis and numerical approximation of singular boundary value problems with the p-Laplacian in fluid mechanics |
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