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Amorphous surface growth via a level set approach. (English) Zbl 1109.35053

The authors construct an equation for amorphous surface growth due to some deposition process within the level set approach and derive a unique viscosity solution to this equation. They develop a theory of convergence of viscosity sub- and super-solutions. Then approximating the equation by parabolic equations with uniformly elliptic part, they prove that the solutions of the approximating equations converge to the viscous solution of the original equation.

MSC:

35K55 Nonlinear parabolic equations
35K65 Degenerate parabolic equations
35Q72 Other PDE from mechanics (MSC2000)
82C24 Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
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