In this paper we investigate a time dependent family of plane closed Jordancurves evolving in the normal direction with a velocity which is assumed to bea function of the curvature, tangential angle and position vector of a curve.We follow the direct approach and analyze the system of governing PDEs forrelevant geometric quantities. We focus on a class of the so-called curvatureadjusted tangential velocities for computation of the curvature driven flow ofplane closed curves. Such a curvature adjusted tangential velocity depends onthe modulus of the curvature and its curve average. Using the theory ofabstract parabolic equations we prove local existence, uniqueness andcontinuation of classical solutions to the system of governing equations. Wefurthermore analyze geometric flows for which normal velocity may depend onglobal curve quantities like the length, enclosed area or total elastic energyof a curve. We also propose a stable numerical approximation scheme based onthe flowing finite volume method. Several computational examples of variousnonlocal geometric flows are also presented in this paper.
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