International Journal of Partial Differential Equations and Applications
ISSN (Print): 2376-9548 ISSN (Online): 2376-9556 Website: Editor-in-chief: Mahammad Nurmammadov
Open Access
Journal Browser
International Journal of Partial Differential Equations and Applications. 2019, 6(1), 13-17
DOI: 10.12691/ijpdea-6-1-2
Open AccessArticle

A Problem of Pursuit Game with Various Constraints on Controls of Players

Fateh Allahabi1, and Mohammad Abdulkawi Mahiub2

1Department of Mathematics, Faculty of Science, Thamar University, Yemen

2Department of Mathematics, Faculty of Science and Arts, Najran University, Saudi Arabia

Pub. Date: November 15, 2019

Cite this paper:
Fateh Allahabi and Mohammad Abdulkawi Mahiub. A Problem of Pursuit Game with Various Constraints on Controls of Players. International Journal of Partial Differential Equations and Applications. 2019; 6(1):13-17. doi: 10.12691/ijpdea-6-1-2


This work introduce a difference controls of players by using a new control method to completing a pursuit game. We study pursuit game problems for controlled partial differential equations of the parabolic type. We proved a theorem on pursuit game with mixed constraints, where pursuers control are subjected to integral (geometric) constraint and geometric (integral) constraint are imposed on evaders control. Moreover, we established the sufficient conditions for which pursuit is possible in the game considered.

pursuit game admissibility control integral constraint geometric constraint

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit


[1]  Ladyzhenskaya, O. A. Boundary-Value Problems of Mathematical Physics, Nauka, Moscow, 1973. [in Russian].
[2]  S. G. Mikhlin, Linear Partial Differential Equations. Vysshaya Shkola, Moscow, 1977. [in Russian].
[3]  Butkovskiy A.G. Control Methods in Systems with Distributed Parameters. Nauka, Moscow, 1975.
[4]  Chernous’ko F.L. Bounded Controls in Systems with Distributed Parameters, Prikl. Mat. Mekh, 56(5). 810-826. 1992.
[5]  Chernousko, F.L. On the Construction of a Bounded Control in Oscillatory Systems. J. Appl. Maths Mechs, 52(4). 426-433.1988.
[6]  Chernousko, F.L. Decomposition and suboptimal control in dynamical systems. J. Appl. Maths Mechs, 54(6). 727-734. 1990.
[7]  M. Tukhtasinov. Some Problems in the Theory of Differential Pursuit Games in Systems with Distributed Parameters. Prikl. Mat. Mekh, 59 (6). 1995.
[8]  N. Yu. Satimov and M. Tukhtasinov, On some game problems for first-order controlled evolution equations, Differential Equations. 41(8). 1169-1177. 2005.
[9]  Satimov N. Yu, and Tukhtasinov M. Game problems on a fixed interval in controlled first-order evolution equations, Mathematical notes. 80(4). 578-589. 2006.
[10]  Ibragimov G.I. A Problem of Optimal Pursuit in Systems with Distributed Parameters. J. Appl. Math. Mech, 66(5). 719-724.
[11]  Ibragimov G.I. Pursuit Differential Game Described by infinite First Order 2-Systems of Differential Equations. Malaysian Journal of Mathematical Sciences. 11(2). 181-190. May. 2017.
[12]  bragimov G.I. Differential Game of Optimal Pursuit for an infinite Systems of Differential Equations. Bulletin of Malaysian Mathematical Sciences Society. 42(1). 391-403. Jun. 2019.