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dc.contributor.authorMonneau, Régis
dc.contributor.authorImbert, Cyril
HAL ID: 9368
ORCID: 0000-0002-1290-8257
dc.contributor.authorForcadel, Nicolas
HAL ID: 171794
ORCID: 0000-0003-4141-8385
dc.descriptionThis new version contains new results: we prove that the weak (viscosity) solutions of the Cauchy problem are in fact smooth. This is a consequence of some gradient estimates in time and space.en
dc.subjectmean curvature motionen
dc.subjectviscosity solutionsen
dc.subjectquasi-linear parabolic equationen
dc.subjectcomparison principleen
dc.subjectmotion of interfacesen
dc.titleUniqueness and existence of spirals moving by forced mean curvature motionen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this paper, we study the motion of spirals by mean curvature type motion in the (two dimensional) plane. Our motivation comes from dislocation dynamics; in this context, spirals appear when a screw dislocation line reaches the surface of a crystal. The first main result of this paper is a comparison principle for the corresponding parabolic quasi-linear equation. As far as motion of spirals are concerned, the novelty and originality of our setting and results come from the fact that, first, the singularity generated by the attached end point of spirals is taken into account for the first time, and second, spirals are studied in the whole space. Our second main result states that the Cauchy problem is well-posed in the class of sub-linear weak (viscosity) solutions. We also explain how to get the existence of smooth solutions when initial data satisfy an additional compatibility condition.en
dc.relation.isversionofjnlnameInterfaces and Free Boundaries
dc.relation.isversionofjnlpublisherEuropean Mathematical Society

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