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WEAK SOLUTION OF A CONTINUUM MODEL FOR VICINAL SURFACE IN THE ATTACHMENT-DETACHMENT-LIMITED REGIME.
- Source :
-
SIAM Journal on Mathematical Analysis . 2017, Vol. 49 Issue 3, p1705-1731. 27p. - Publication Year :
- 2017
-
Abstract
- We study in this work a continuum model derived from a one-dimensional attachmentdetachment-limited type step ow on a vicinal surface, ut = -u2(u3)hhhh; where u, considered as a function of step height h, is the step slope of the surface. We formulate a notion of a weak solution to this continuum model and prove the existence of a global weak solution, which is positive almost everywhere. We also study the long time behavior of the weak solution and prove it converges to a constant solution as time goes to infinity. The space-time Hölder continuity of the weak solution is also discussed as a byproduct. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00361410
- Volume :
- 49
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Mathematical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 123900316
- Full Text :
- https://doi.org/10.1137/16M1094543