Dynamic search in three-dimensional convex domains (Q5947811)

A motion of two point objects - A (searching) and B (escaping) in a domain \(\Omega\) \((\Omega \subset R^n)\) is considered. The velocity of the first object (A) is constant in the absolute value and is equal to \(\alpha\) \((\alpha > 0)\), as to the velocity of the second object (B) it is less or equal to \(\beta\) \((\beta \geq 0)\). The A-object is tending to recognize the B-object, i.e. shorten a distance between the objects to a given magnitude \(l\) \((l\geq 0)\). The main goal of the investigation is to find sufficient conditions of realizability of the search and to construct a search trajectory in a three-dimensional circle cylinder. Then a solution of the search problem in the three-dimensional convex domains can be obtained as simple consequences of the previous results. The results can be also generalized for spaces of an arbitrary dimensions.