# American Institute of Mathematical Sciences

September  2018, 8(3&4): 809-828. doi: 10.3934/mcrf.2018036

## Optimal control problems for some ordinary differential equations with behavior of blowup or quenching

 1 School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China 2 Mathematics & Science College, Shanghai Normal University, Shanghai 200234, China

* Corresponding author: Weihan Wang

Received  October 2017 Revised  January 2018 Published  September 2018

Fund Project: This work was supported in part by National Natural Science Foundation of China under grant 11701376 and 11471070, and School Foundation of Shanghai Normal University under grant SK201713.

This paper is concerned with some optimal control problems for equations with blowup or quenching property. We first study the existence and Pontryagin's maximum principle for optimal controls which have the minimal energy among all the controls whose corresponding solutions blow up at the right-hand time end-point of a given functional. Then, the same problem for quenching case is discussed. Finally, we establish Pontryagin's maximum principle for optimal controls of extended problems after quenching.

Citation: Ping Lin, Weihan Wang. Optimal control problems for some ordinary differential equations with behavior of blowup or quenching. Mathematical Control & Related Fields, 2018, 8 (3&4) : 809-828. doi: 10.3934/mcrf.2018036
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