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Volumn 37, Issue 2, 2006, Pages 372-410

On a Hele-Shaw-type domain evolution with convected surface energy density

Author keywords

Degenerate nonlocal parabolic evolution; Free boundary motion

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; GALERKIN METHODS; MATHEMATICAL MODELS; PROBLEM SOLVING; SURFACE TENSION; VECTOR QUANTIZATION;

EID: 33644946082     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141004444846     Document Type: Article
Times cited : (8)

References (21)
  • 1
    • 0029656405 scopus 로고    scopus 로고
    • Singularity formation in Hele-Shaw bubbles
    • R. ALMGREN, Singularity formation in Hele-Shaw bubbles, Phys. Fluids, 8 (1996), pp. 344-352.
    • (1996) Phys. Fluids , vol.8 , pp. 344-352
    • Almgren, R.1
  • 2
    • 0032136390 scopus 로고    scopus 로고
    • On the Cauchy problem for a capillary drop. Part I: Irrotational motion
    • K. BEYBR AND M. GÜNTHER, On the Cauchy problem for a capillary drop. Part I: Irrotational motion, Math. Methods Appl. Sci., 21 (1998), pp. 1149-1183.
    • (1998) Math. Methods Appl. Sci. , vol.21 , pp. 1149-1183
    • Beybr, K.1    Günther, M.2
  • 3
    • 17444410916 scopus 로고    scopus 로고
    • The Jacobi equation for irrotational free boundary flows
    • K. BEYER AND M. GÜNTHER, The Jacobi equation for irrotational free boundary flows, Analysis, 20 (2000), pp. 237-254.
    • (2000) Analysis , vol.20 , pp. 237-254
    • Beyer, K.1    Günther, M.2
  • 4
    • 0000851461 scopus 로고
    • Global solution for small data to the Hele-Shaw problem
    • P. CONSTANTIN AND M. PUGH, Global solution for small data to the Hele-Shaw problem, Non-linearity, 6 (1993), pp. 393-415.
    • (1993) Non-linearity , vol.6 , pp. 393-415
    • Constantin, P.1    Pugh, M.2
  • 5
    • 33644936112 scopus 로고    scopus 로고
    • Local and global existence results for anisotropic Hele-Shaw flows
    • K. DECKELNIOK AND C. ELLIOTT, Local and global existence results for anisotropic Hele-Shaw flows, Proc. Roy. Soc. Edinburgh Sect. A, 129 (1999), pp. 265-294.
    • (1999) Proc. Roy. Soc. Edinburgh Sect. A , vol.129 , pp. 265-294
    • Deckelniok, K.1    Elliott, C.2
  • 6
    • 0001025274 scopus 로고    scopus 로고
    • A center manifold analysis for the Mullins-Sekerka model
    • J. ESCHER AND G. SIMONETT, A center manifold analysis for the Mullins-Sekerka model, J. Differential Equations, 143 (1998), pp. 267-292.
    • (1998) J. Differential Equations , vol.143 , pp. 267-292
    • Escher, J.1    Simonett, G.2
  • 7
    • 0000990726 scopus 로고    scopus 로고
    • Nonlinear stability of a quasi-static Stefan problem with surface tension: A continuation approach
    • A. FRIEDMAN AND F. REITICH, Nonlinear stability of a quasi-static Stefan problem with surface tension: A continuation approach, Ann. Spuola Norm. Sup. Pisa Cl. Sci. (4), 30 (2001), pp. 341-403.
    • (2001) Ann. Spuola Norm. Sup. Pisa Cl. Sci. (4) , vol.30 , pp. 341-403
    • Friedman, A.1    Reitich, F.2
  • 8
    • 0346491845 scopus 로고    scopus 로고
    • Variational formulation for the lubrication approximation of the Hele-Shaw flow
    • L. GIACOMELLI AND F. OTTO, Variational formulation for the lubrication approximation of the Hele-Shaw flow, Calc. Var. Partial Differential Equations, 3 (2001), pp. 377-403.
    • (2001) Calc. Var. Partial Differential Equations , vol.3 , pp. 377-403
    • Giacomelli, L.1    Otto, F.2
  • 10
    • 21644445060 scopus 로고    scopus 로고
    • On Stokes flow with variable and degenerate surface tension coefficient
    • M. GÜNTHER AND G. PROKERT, On Stokes flow with variable and degenerate surface tension coefficient, NODEA Nonlinear Differential Equations Appl., 12 (2005), pp. 21-60.
    • (2005) NODEA Nonlinear Differential Equations Appl. , vol.12 , pp. 21-60
    • Günther, M.1    Prokert, G.2
  • 11
    • 84974250737 scopus 로고
    • On classical solvability for the Hele-Shaw moving boundary problems with kinetic undercooling regularisation
    • YU. E. HOHLOV AND M. REISSIG, On classical solvability for the Hele-Shaw moving boundary problems with kinetic undercooling regularisation, European J. Appl. Math., 6 (1995), pp. 421-439.
    • (1995) European J. Appl. Math. , vol.6 , pp. 421-439
    • Hohlov, Yu.E.1    Reissig, M.2
  • 12
    • 0017190112 scopus 로고
    • The boundary problems of physical geodesy
    • L. HÖRMANDER, The boundary problems of physical geodesy, Arch. Ration. Mech. Anal., 62 (1976), pp. 1-52.
    • (1976) Arch. Ration. Mech. Anal. , vol.62 , pp. 1-52
    • Hörmander, L.1
  • 13
    • 84971920974 scopus 로고
    • Complex variable methods in Hele-Shaw moving boundary problems
    • S. D. HOWISON, Complex variable methods in Hele-Shaw moving boundary problems, European J. Applied Math., 3 (1992), pp. 209-224.
    • (1992) European J. Applied Math. , vol.3 , pp. 209-224
    • Howison, S.D.1
  • 14
    • 0003134154 scopus 로고
    • Nonlinear evolution equations and the Euler flow
    • T. KATO AND C. Y. LAI, Nonlinear evolution equations and the Euler flow, J. Funct. Anal., 56 (1984), pp. 15-28.
    • (1984) J. Funct. Anal. , vol.56 , pp. 15-28
    • Kato, T.1    Lai, C.Y.2
  • 15
    • 0027974881 scopus 로고
    • The influence of surfactant on the bubble motion in Hele-Shaw cells
    • S. R. K. MARUVADA, C. W. PARK, AND D. Y. YOON, The influence of surfactant on the bubble motion in Hele-Shaw cells, Phys. Fluids, 6 (1994), pp. 3267-3275.
    • (1994) Phys. Fluids , vol.6 , pp. 3267-3275
    • Maruvada, S.R.K.1    Park, C.W.2    Yoon, D.Y.3
  • 16
    • 0033264395 scopus 로고    scopus 로고
    • Hyperbolic evolution equations for moving boundary problems
    • G. PROKERT, Hyperbolic evolution equations for moving boundary problems, European J. Applied Math., 10 (1999), pp. 607-622.
    • (1999) European J. Applied Math. , vol.10 , pp. 607-622
    • Prokert, G.1
  • 17
    • 20444447761 scopus 로고    scopus 로고
    • On Stokes flow driven by surface tension in the presence of a surfactant
    • G. PROKERT, On Stokes flow driven by surface tension in the presence of a surfactant, European J. Applied Math., 15 (2004), pp. 791-819.
    • (2004) European J. Applied Math. , vol.15 , pp. 791-819
    • Prokert, G.1
  • 19
    • 0022888394 scopus 로고
    • Viscous fingering in Hele-Shaw cells
    • P. G. SAFFMAN, Viscous fingering in Hele-Shaw cells, J. Fluid Mech., 173 (1986), pp. 73-94.
    • (1986) J. Fluid Mech. , vol.173 , pp. 73-94
    • Saffman, P.G.1
  • 20
    • 21444444714 scopus 로고    scopus 로고
    • Asymptotic behaviour of the solutions of the supercooled Stefan problem
    • F. YI, Asymptotic behaviour of the solutions of the supercooled Stefan problem, Proc. Roy. Soc. Edinburgh Sect. A, 127 (1997), pp. 181-190.
    • (1997) Proc. Roy. Soc. Edinburgh Sect. A , vol.127 , pp. 181-190
    • Yi, F.1
  • 21
    • 0347105107 scopus 로고    scopus 로고
    • A quasisteady Stefan problem with curvature correction and kinetic undercooling
    • W. YU, A quasisteady Stefan problem with curvature correction and kinetic undercooling, J. Partial Differential Equations, 9 (1996), pp. 55-70.
    • (1996) J. Partial Differential Equations , vol.9 , pp. 55-70
    • Yu, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.