This paper is concerned with the exact null controllability of certain semilinear Black-Scholes type equations in a bounded interval of R + with Neumann boundary conditions. The control is assumed to be distributed along a subset ω of I. First, we prove the exact null controllability of an associated linearized problem by establishing the observability estimate derived from a Carleman type inequality which is the key result for the whole theory. Then, the exact null controllability of the nonlinear problem is discussed using the infinite-dimensional Kakutani fixed point theorem.
Bibliographical noteFunding Information:
The work of the first author was supported by the Brain Korea 21 project at Yonsei University, 2008. The work of the fourth author was financially supported by the Ministry of Knowledge Economy (MKE) and Korea Industrial Technology Foundation (KOTEF) through the Human Resource Training Project for Strategic Technology, 2008.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computer Science Applications