Pulsating wave for mean curvature flow in inhomogeneous medium

Dirr, Nicolas P. ORCID: https://orcid.org/0000-0003-3634-7367, Karali, G. and Yip, N. K. 2008. Pulsating wave for mean curvature flow in inhomogeneous medium. European Journal of Applied Mathematics 19 (6) , pp. 661-699. 10.1017/S095679250800764X

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Abstract

We prove the existence and uniqueness of pulsating waves for the motion by mean curvature of an n-dimensional hypersurface in an inhomogeneous medium, represented by a periodic forcing. The main difficulty is caused by the degeneracy of the equation and the fact the forcing is allowed to change sign. Under the assumption of weak inhomogeneity, we obtain uniform oscillation and gradient bounds so that the evolving surface can be written as a graph over a reference hyperplane. The existence of an effective speed of propagation is established for any normal direction. We further prove the Lipschitz continuity of the speed with respect to the normal and various stability properties of the pulsating wave. The results are related to the homogenisation of mean curvature flow with forcing.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Additional Information:	Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/0956-7925/ (accessed 25/02/2014).
Publisher:	Cambridge University Press
ISSN:	0956-7925
Date of First Compliant Deposit:	30 March 2016
Last Modified:	07 May 2023 14:51
URI:	https://orca.cardiff.ac.uk/id/eprint/13063

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