On the longtime behavior of solutions to a model for epitaxial growth

zbMath1233.35036MaRDI QIDQ663530

Gianluca Mola, Atsushi Yagi, Maurizio Grasselli

Publication date: 17 February 2012

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ojm/1326291214

zbMATH Keywords

Łojasiewicz-Simon inequalitydissipative dynamical systemno-flux boundary conditionstwo space dimension

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) Initial-boundary value problems for higher-order parabolic equations (35K35) Thin fluid films (76A20) Quasilinear parabolic equations (35K59)

Related Items (13)

Convergence of solutions of a nonlocal biharmonic MEMS equation with the fringing field ⋮ Lifespan of solutions to a fourth order parabolic PDE involving the Hessian modeling epitaxial growth ⋮ A B-spline finite element method for nonlinear differential equations describing crystal surface growth with variable coefficient ⋮ Energetics and coarsening analysis of a simplified non-linear surface growth model ⋮ Pointwise error estimate of the compact difference methods for the fourth‐order parabolic equations with the third Neumann boundary conditions ⋮ The compact difference approach for the fourth‐order parabolic equations with the first Neumann boundary value conditions ⋮ Well-posedness and dynamic properties of solutions to a class of fourth order parabolic equation with mean curvature nonlinearity ⋮ Global existence versus blow-up results for a fourth order parabolic PDE involving the Hessian ⋮ Global attractor for a nonlinear model with periodic boundary value condition ⋮ Optimal control problem for the BCF model describing crystal surface growth ⋮ Optimal control for a higher-order nonlinear parabolic equation describing crystal surface growth ⋮ Global dynamics of a fourth-order parabolic equation describing crystal surface growth ⋮ FINITE ELEMENT METHOD FOR A NONLINEAR DIFFERENTIAL EQUATION DESCRIBING CRYSTAL SURFACE GROWTH

Cites Work

• Epitaxial growth without slope selection: energetics, coarsening, and dynamic scaling
• Unconditionally stable schemes for equations of thin film epitaxy
• Regularity results for elliptic equations in Lipschitz domains
• A simple unified approach to some convergence theorems of L. Simon
• A fourth-order parabolic equation modeling epitaxial thin film growth
• Convergence for semilinear degenerate parabolic equations in several space dimensions
• Finitely many solutions for a class of boundary value problems with superlinear convex non\-linearity
• Exponential attractors for a nonlinear reaction-diffusion system in
• Thin film epitaxy with or without slope selection
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