Non-perturbative semi-analytical source-type solutions of thin-film equation

Abstract We employ Adomian’s decomposition method to explicitly construct approximate non-perturbative source-like solutions of the thin-film equation h t  = −( h n h xxx ) x for 0  n

[1]  John R. King,et al.  Dipoles and similarity solutions of the thin film equation in the half-line , 2000 .

[2]  A. Friedman,et al.  Higher order nonlinear degenerate parabolic equations , 1990 .

[3]  Y. Cherruault,et al.  New results of convergence of Adomian’s method , 1999 .

[4]  Stephen Wolfram,et al.  Mathematica: a system for doing mathematics by computer (2nd ed.) , 1991 .

[5]  Bruce W. Char,et al.  Maple V Language Reference Manual , 1993, Springer US.

[6]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[7]  H. S. Hele-Shaw,et al.  The Flow of Water , 1898, Nature.

[8]  Walter Oevel,et al.  Das MuPAD Tutorium , 2000 .

[9]  Harald Garcke,et al.  On A Fourth-Order Degenerate Parabolic Equation: Global Entropy Estimates, Existence, And Qualitativ , 1998 .

[10]  Symmetry reductions and new exact invariant solutions of the generalized Burgers equation arising in nonlinear acoustics , 2004 .

[11]  Tim G. Myers,et al.  Thin Films with High Surface Tension , 1998, SIAM Rev..

[12]  Abdul-Majid Wazwaz,et al.  The modified decomposition method and Padé approximants for solving the Thomas-Fermi equation , 1999, Appl. Math. Comput..

[13]  G. Grün Degenerate Parabolic Differential Equations of Fourth Order and a Plasticity Model with Non-Local Hardening , 1995 .

[14]  Y. Cherruault Convergence of Adomian's method , 1989 .

[15]  C. M. Elliott,et al.  On the Cahn-Hilliard equation with degenerate mobility , 1996 .