메뉴 건너뛰기




Volumn 87, Issue 1, 2000, Pages 113-152

Nonnegativity preserving convergent schemes for the thin film equation

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0034553999     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110000197     Document Type: Article
Times cited : (123)

References (22)
  • 1
    • 0032357417 scopus 로고    scopus 로고
    • Finite element approximation of a fourth order nonlinear degenerate parabolic equation
    • J. Barrett, J. Blowey, and H. Garcke. Finite element approximation of a fourth order nonlinear degenerate parabolic equation. Numer. Math. 80(4), 525-556 (1998)
    • (1998) Numer. Math. , vol.80 , Issue.4 , pp. 525-556
    • Barrett, J.1    Blowey, J.2    Garcke, H.3
  • 2
    • 21844510002 scopus 로고
    • Nonnegative solutions of a fourth order nonlinear degenerate parabolic equation
    • E. Beretta, M. Bertsch, and R. Dal Passo. Nonnegative solutions of a fourth order nonlinear degenerate parabolic equation. Arch. Rat. Mech. Anal. 129:175-200 (1995)
    • (1995) Arch. Rat. Mech. Anal. , vol.129 , pp. 175-200
    • Beretta, E.1    Bertsch, M.2    Dal Passo, R.3
  • 3
    • 0008858823 scopus 로고
    • Viscous flows, fourth order nonlinear degenerate parabolic equations and singular elliptic problems
    • J.I. Diaz, M.A. Herrero, A. Linan, and J.L. Vazquez, editors, Free boundary problems: theory and applications, Longman, Harlow
    • F. Bernis. Viscous flows, fourth order nonlinear degenerate parabolic equations and singular elliptic problems. In J.I. Diaz, M.A. Herrero, A. Linan, and J.L. Vazquez, editors, Free boundary problems: theory and applications, Pitman Research Notes in Mathematics 323, pages 40-56. Longman, Harlow (1995)
    • (1995) Pitman Research Notes in Mathematics , vol.323 , pp. 40-56
    • Bernis, F.1
  • 4
    • 0000254565 scopus 로고    scopus 로고
    • Finite speed of propagation and continuity of the interface for thin viscous flows
    • F. Bernis. Finite speed of propagation and continuity of the interface for thin viscous flows. Adv. Diff. Equations 1(3) 337-368 (1996)
    • (1996) Adv. Diff. Equations , vol.1 , Issue.3 , pp. 337-368
    • Bernis, F.1
  • 5
    • 0001057861 scopus 로고    scopus 로고
    • Finite speed of propagation for thin viscous flows when 2 ≤ n < 3
    • F. Bernis. Finite speed of propagation for thin viscous flows when 2 ≤ n < 3. C.R. Acad. Sci. Paris; Sér.I Math. 322 (1996)
    • (1996) C.R. Acad. Sci. Paris; Sér.I Math. , vol.322
    • Bernis, F.1
  • 6
    • 21444453183 scopus 로고    scopus 로고
    • The free boundary of thin viscous flows
    • Proceedings of ICIAM'95
    • F. Bernis. The Free Boundary of Thin Viscous Flows, Proceedings of ICIAM'95. Z. Angew. Math.Mech. 76 Suppl. 2, 369-372 (1996)
    • (1996) Z. Angew. Math.Mech. , vol.76 , Issue.SUPPL. 2 , pp. 369-372
    • Bernis, F.1
  • 7
    • 0031487592 scopus 로고    scopus 로고
    • Source-type solutions to thin-film equations in higher space dimensions
    • F. Bernis and R. Ferreira. Source-type solutions to thin-film equations in higher space dimensions. Euro. J. Appl. Math. 8, 507-524 (1997)
    • (1997) Euro. J. Appl. Math. , vol.8 , pp. 507-524
    • Bernis, F.1    Ferreira, R.2
  • 8
    • 45149137344 scopus 로고
    • Higher order nonlinear degenerate parabolic equations
    • F. Bernis and A. Friedman. Higher order nonlinear degenerate parabolic equations. J. Diff. Equ. 83, 179-206 (1990)
    • (1990) J. Diff. Equ. , vol.83 , pp. 179-206
    • Bernis, F.1    Friedman, A.2
  • 9
    • 0001460885 scopus 로고
    • Source-type solutions of a fourth order nonlinear degenerate parabolic equations
    • F. Bernis, L.A. Peletier, and S.M. Williams. Source-type solutions of a fourth order nonlinear degenerate parabolic equations. Nonlin. Anal. 18, 217-234 (1992)
    • (1992) Nonlin. Anal. , vol.18 , pp. 217-234
    • Bernis, F.1    Peletier, L.A.2    Williams, S.M.3
  • 10
    • 0040488514 scopus 로고    scopus 로고
    • The lubrication approximation for thin viscous films: Regularity and long time behaviour of weak solutions
    • A.L. Bertozzi and M. Pugh. The lubrication approximation for thin viscous films: regularity and long time behaviour of weak solutions. Comm. Pure Appl. Maht. 49(2), 85-123 (1996)
    • (1996) Comm. Pure Appl. Maht. , vol.49 , Issue.2 , pp. 85-123
    • Bertozzi, A.L.1    Pugh, M.2
  • 11
    • 84894616360 scopus 로고    scopus 로고
    • The thin viscous flow equation in higher space dimensions
    • M. Bertsch, R. Dal Passo, H. Garcke, and G. Grün. The thin viscous flow equation in higher space dimensions. Adv. Diff. Equ. 3, 417-440 (1998)
    • (1998) Adv. Diff. Equ. , vol.3 , pp. 417-440
    • Bertsch, M.1    Dal Passo, R.2    Garcke, H.3    Grün, G.4
  • 13
    • 0032367668 scopus 로고    scopus 로고
    • On a fourth order degenerate parabolic equation: Global entropy estimates and qualitative behaviour of solutions
    • R. Dal Passo, H. Garcke, and G. Grün. On a fourth order degenerate parabolic equation: global entropy estimates and qualitative behaviour of solutions. SIAM J. Math. Anal. 29, 321-342 (1998)
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 321-342
    • Dal Passo, R.1    Garcke, H.2    Grün, G.3
  • 14
    • 0016091290 scopus 로고
    • On the motion of a fluid-fluid interface along a solid surface
    • E.B. Dussan and S. Davis. On the motion of a fluid-fluid interface along a solid surface. J. Fluid Mech. 65, 71-95 (1974)
    • (1974) J. Fluid Mech. , vol.65 , pp. 71-95
    • Dussan, E.B.1    Davis, S.2
  • 15
    • 0030526461 scopus 로고    scopus 로고
    • On the cahn-hilliard equation with degenerate mobility
    • C.M. Elliott and H. Garcke. On the cahn-hilliard equation with degenerate mobility. SIAM J. Math.Anal. 27(2), 404-423 (1996)
    • (1996) SIAM J. Math.Anal. , vol.27 , Issue.2 , pp. 404-423
    • Elliott, C.M.1    Garcke, H.2
  • 16
    • 0001520476 scopus 로고
    • Degenerate parabolic equations of fourth order and a plasticity model with nonlocal hardening
    • G. Grün. Degenerate parabolic equations of fourth order and a plasticity model with nonlocal hardening. Z. Anal. Anwendungen 14, 541-573 (1995)
    • (1995) Z. Anal. Anwendungen , vol.14 , pp. 541-573
    • Grün, G.1
  • 17
    • 0007245075 scopus 로고    scopus 로고
    • Lubrication approximation with prescribed non-zero contact angle: An existence result
    • F. Otto. Lubrication approximation with prescribed non-zero contact angle: an existence result. Comm. Part. Diff. Equ. 23, 2077-2164 (1998)
    • (1998) Comm. Part. Diff. Equ. , vol.23 , pp. 2077-2164
    • Otto, F.1
  • 20
    • 0020845295 scopus 로고
    • Spreading of droplets of nonvolatile liquids over a flat solid
    • V.M. Starov. Spreading of droplets of nonvolatile liquids over a flat solid. J. Colloid Interface Sci. UdSSR 45 (1983)
    • (1983) J. Colloid Interface Sci. UdSSR , vol.45
    • Starov, V.M.1
  • 21
    • 0000005482 scopus 로고
    • A fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems
    • H. A. van der Vorst. A fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comp. 13, 73-86 (1992)
    • (1992) SIAM J. Sci. Stat. Comp. , vol.13 , pp. 73-86
    • Van Der Vorst, H.A.1
  • 22
    • 0000708355 scopus 로고    scopus 로고
    • Positivity preserving numerical schemes for lubrication-type equations
    • L. Zhornitskaya and A.L. Bertozzi. Positivity preserving numerical schemes for lubrication-type equations. SIAM J. Num. Anal. 37(2), 523-555 (2000)
    • (2000) SIAM J. Num. Anal. , vol.37 , Issue.2 , pp. 523-555
    • Zhornitskaya, L.1    Bertozzi, A.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.