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The paper is devoted to studying a fourth-order degenerate parabolic equation, which arises in fluid, phase transformation and biology. Based on the existence and uniqueness of one semi-discrete problem, two types of approximate solutions are introduced. By establishing some necessary uniform estimates for those approximate solutions, the existence and uniqueness of the corresponding parabolic problem are obtained.
Moreover, the long time asymptotic behavior is established by the entropy functional method.
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참고문헌 (11)
참고문헌 신청
B. Liang / 2008 / Existence and asymptotic behavior of solutions to a nonlinear parabolic equation of fourth-order / J. Math. Anal. Appl 348 (1) : 234 ~ 243
D. Gilbarg / 1983 / Elliptic Partial Different Equations of Second Order / Springer-Verlag
F. Bernis / 1990 / Higher order nonlinear degenerate parabolic equations / J. Differential Equations 83 (1) : 179 ~ 206
G. Gr¨un / 1995 / Degenerate parabolic differential equations of fourth order and a plasticity model with nonlocal hardening / Z. Anal. Anwendungen 14 (3) : 541 ~ 574
J. A. Carrillo / 2002 / Long-time asymptotics for strong solutions of the thin film equation / Commu. Math. Phys 225 (3) : 551 ~ 571
D. Gilbarg / 1983 / Elliptic Partial Different Equations of Second Order / Springer-Verlag
F. Bernis / 1990 / Higher order nonlinear degenerate parabolic equations / J. Differential Equations 83 (1) : 179 ~ 206
G. Gr¨un / 1995 / Degenerate parabolic differential equations of fourth order and a plasticity model with nonlocal hardening / Z. Anal. Anwendungen 14 (3) : 541 ~ 574
J. A. Carrillo / 2002 / Long-time asymptotics for strong solutions of the thin film equation / Commu. Math. Phys 225 (3) : 551 ~ 571
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