4,086 research outputs found
Characterizing the stabilization size for semi-implicit Fourier-spectral method to phase field equations
Recent results in the literature provide computational evidence that
stabilized semi-implicit time-stepping method can efficiently simulate phase
field problems involving fourth-order nonlinear dif- fusion, with typical
examples like the Cahn-Hilliard equation and the thin film type equation. The
up-to-date theoretical explanation of the numerical stability relies on the
assumption that the deriva- tive of the nonlinear potential function satisfies
a Lipschitz type condition, which in a rigorous sense, implies the boundedness
of the numerical solution. In this work we remove the Lipschitz assumption on
the nonlinearity and prove unconditional energy stability for the stabilized
semi-implicit time-stepping methods. It is shown that the size of stabilization
term depends on the initial energy and the perturba- tion parameter but is
independent of the time step. The corresponding error analysis is also
established under minimal nonlinearity and regularity assumptions
Gradient bounds for a thin film epitaxy equation
We consider a gradient flow modeling the epitaxial growth of thin films with
slope selection. The surface height profile satisfies a nonlinear diffusion
equation with biharmonic dissipation. We establish optimal local and global
wellposedness for initial data with critical regularity. To understand the
mechanism of slope selection and the dependence on the dissipation coefficient,
we exhibit several lower and upper bounds for the gradient of the solution in
physical dimensions
Structural Origins of the Enhancement in Ionic Conductivity of a Chalcogenide Compound by Adding AgI
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