Journal of East China Normal University(Natural Science) >

2018 , Vol. 2018 >Issue 1: 1 - 10

DOI: https://doi.org/10.3969/j.issn.1000-5641.2018.01.001

A free boundary problem in variational inequality with gradient constraint

  • GUAN Chong-hu ,
  • CHEN Jing
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  • 1. School of Mathematics, Jiaying University, Meizhou Guangdong 514015, China;
    2. School of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong 999077, China

Received date: 2017-02-15

  Online published: 2018-01-11

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Abstract

Consider a parabolic variational inequality with gradient constraint
min{vt-1/2σ2vxx-μvx+cv,vx-1}=0.
The problem stems from a stochastic optimal control problem based on optimal dividend model. By using PDE technique and the penalty method, the existence and uniqueness and some a priori estimates of the solution of the variational inequality are obtained, and then the properties of the free boundary are further discussed. It is proved that the free boundary can be expressed as a function of x with respect to t and is a monotonically increasing, C∞ smooth curve starting from zero.

Key words： gradient constraint; variational inequality; free boundary; stochastic optimal control; optimal dividend

Cite this article

GUAN Chong-hu , CHEN Jing . A free boundary problem in variational inequality with gradient constraint[J]. Journal of East China Normal University(Natural Science), 2018 , 2018(1) : 1 -10 . DOI: 10.3969/j.issn.1000-5641.2018.01.001

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