Abstract
We consider the motion of an object t in the space ℝ2, where a bodily bounded set G with piecewise smooth boundary hinders the motion and visibility. In a neighborhood of convex parts of the boundary, there are observers, which can hide from t in a shading set s(t) ⊂ ℝ2 G in the case of danger from t. We find characteristic properties of a trajectory T of the object that maximizes the value min{ρ(t, s(t)): t ∈ T}.
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References
V. I. Berdyshev, “On the problem of tracking a moving object by observers,” Proc. Steklov Inst. Math. 289 (Suppl. 1), S42–S53 (2015).
V. I. Berdyshev, “A letter to the Editor,” Trudy Inst. Mat. Mekh. UrO RAN 21 (4), 316 (2015).
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Original Russian Text © V.I. Berdyshev, 2015, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Vol. 21, No. 4.
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Berdyshev, V.I. A moving object and observers in ℝ2 with a piecewise smooth shading set. Proc. Steklov Inst. Math. 296 (Suppl 1), 95–101 (2017). https://doi.org/10.1134/S0081543817020092
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DOI: https://doi.org/10.1134/S0081543817020092