Global existence of solutions of area-preserving curvature flow of a convex plane curve in an inhomogeneous medium

R. Lui () and H. Ninomiya ()
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R. Lui: Worcester Polytechnic Institute
H. Ninomiya: Meiji University

Partial Differential Equations and Applications, 2022, vol. 3, issue 3, 1-16

Abstract: Abstract Consider a two-dimensional region whose boundary is a non-self-intersecting closed curve, which is called an interface. Suppose the movement of the region is governed only by forces on its boundary so that the area of the region is preserved. An area-preserving curvature flow is the special case when the force is dependent on the curvature of the interface. In a homogeneous medium, Gage showed that an initially convex interface remains convex and converges to a stationary circle. However, in applications, the medium is often not homogeneous and the interface moves towards a more favorable environment. The properties of the medium are described by a signal function that is a twice continuously differentiable function defined on the plane. This paper is devoted to proving the global existence of interfaces under the assumption that the Hessian of the signal function is negative definite.

Keywords: 35A01; 35K93; 53A04; 53C44 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s42985-022-00176-1

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