We discuss short time existence for a surface diffusion evolution equation with curvature regularization in the context of epitaxially strained three-dimensional films. This is achieved by implementing a minimizing movement scheme, which is hinged on the $H^{-1}$-gradient flow structure underpinning the evolution law. Long-time behavior and Liapunov stability in the case of initial data close to a flat configuration are also addressed.
Motion of elastic thin films by anisotropic surface diffusion with curvature regularization / Fusco, Nicola. - (2014). (Intervento presentato al convegno ERC Workshop on Existence and Regularity for Nonlinear Systems of Partial Differential Equations tenutosi a Pisa nel 30 giugno - 5 luglio2014).
Motion of elastic thin films by anisotropic surface diffusion with curvature regularization
FUSCO, NICOLA
2014
Abstract
We discuss short time existence for a surface diffusion evolution equation with curvature regularization in the context of epitaxially strained three-dimensional films. This is achieved by implementing a minimizing movement scheme, which is hinged on the $H^{-1}$-gradient flow structure underpinning the evolution law. Long-time behavior and Liapunov stability in the case of initial data close to a flat configuration are also addressed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
