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In this paper we study a flow by minkowskian curvature where we have a different Minkowski plane at each time. We derive some evolution formulas, present sufficient hypotesis for the short time existence and convexity of solutions and study the motion considering a particular type of families of Minkowski norms. Also, as a corollary we establish a result about a certain family of nonlinear parabolic PDE's., Comment: 9 pages

In this paper we study the curvature flow of a curve in a plane endowed with a minkowskian norm whose unit ball is smooth. We show that many of the properties known in the euclidean case can be extended (with due adaptations) to this new situation. In particular, we show that simple, closed, strictly convex, smooth curves remain so until the area enclosed by them vanishes. Moreover, their isoperimetric ratios converge to the minimum possible value, only attained by the minkowskian circle - so these curves converge to a minkowskian "circular point" as the enclosed area approaches zero., Comment: 18 pages, 2 figures