Geodesic
Dynamical system for BCF model describing crystal surface growth
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 10 (2008), pp. 75-88

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This paper treats the initial-boundary value problem for a nonlinear parabolic equation of forth order which was presented by Johnson — Orme — Hunt — Graff — Sudijono — Sauder — Orr [1] in order to describe the interesting phenomena of crystal surface growth under molecular beam epitaxy (MBE). First we construct unique local solutions in a suitable function space by applying the techniques of abstract parabolic evolution equations. Second we establish a priori estimates to obtain the global existence of solutions. Our goal is then to construct a dynamical system determined from the initial-boundary value problem of the model equation.
Keywords: Dynamical system, BCF model, semilinear parabolic equation, a priori estimate. 
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     author = {H. Fujimura and A. Yagi},
     title = {Dynamical system for {BCF} model describing crystal  surface growth},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {75--88},
     publisher = {mathdoc},
     number = {10},
     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/VCHGU_2008_10_a10/}
}
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H. Fujimura; A. Yagi. Dynamical system for BCF model describing crystal  surface growth. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 10 (2008), pp. 75-88. http://geodesic.mathdoc.fr/item/VCHGU_2008_10_a10/