# The -catch problem with two players under exponentially damping geometric constraints

## The -catch problem with two players under exponentially damping geometric constraints

## Abstract

Annotation. We examine the -catch and -escape problems in a differential game involving two players - a pursuer and an evader - with inertial movements. Both players are subject to exponential damping geometric constraints on their controls, meaning that the magnitudes of their acceleration vectors decrease monotonically over time. In the -catch problem, we construct an approach strategy for the pursuer, which aims to bring the pursuer within a distance of the evader (where ). We alsom define a sufficient condition for -catch. In the -escape problem, we propose a specific admissiblestrategy for the evader and identify a sufficient condition for successful evasion.

## References

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Turgunboeva M.A., (2023) -catch and -escape differential games with non-inertial objects under non-stationary geometric constraints on controls. Uzbek Mathematical Journal. Vol. 67, No. 4, P. 100-

## Published

## How to Cite

*MODERN PROBLEMS AND PROSPECTS OF APPLIED MATHEMATICS*,

*1*(01). Retrieved from https://ojs.qarshidu.uz/index.php/mp/article/view/544