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The converge of Euler polygons to noncontinuable solutions


There is studied the possibility of approximation of nonextendable solutions on the domain by Euler's polygonal curves consisting of countable sets of line segments. Convergence is understood in the sense of graphs convergence in the Hausforff metric. It is shown that if a solution of the auxiliary system is integrably stable and the integral of curvature taken along its graph is finite, then for approximation it is sufficient to tend the size of polyline segments to zero.


euler's polygonal curves, nonextendable solutions; approximation in the Hausdorff metric; integral stability

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519.622.2, 517.925.52



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