A class of fourth-order nonlinear parabolic equations modeling the epitaxial growth of thin films
Yang Liu, Wenke Li
Abstract
<p style='text-indent:20px;'>In this paper, the initial-boundary value problem for a class of fourth-order nonlinear parabolic equations modeling the epitaxial growth of thin films is studied. By means of the theory of potential wells, the global existence, asymptotic behavior and finite time blow-up of weak solutions are obtained.
Topics & Concepts
Nonlinear systemClass (philosophy)Boundary value problemMathematicsMathematical analysisOrder (exchange)Parabolic partial differential equationEpitaxyValue (mathematics)PhysicsMaterials sciencePartial differential equationLayer (electronics)Computer scienceQuantum mechanicsComposite materialStatisticsFinanceArtificial intelligenceEconomicsFluid Dynamics and Thin FilmsSolidification and crystal growth phenomenaTheoretical and Computational Physics