Exact null controllability of a semilinear parabolic equation arising in finance

K. Sakthivel; G. Devipriya; K. Balachandran; J. H. Kim

doi:10.1016/j.nahs.2009.04.007

Exact null controllability of a semilinear parabolic equation arising in finance

K. Sakthivel, G. Devipriya, K. Balachandran, J. H. Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	565-577
Number of pages	13
Journal	Nonlinear Analysis: Hybrid Systems
Volume	3
Issue number	4
DOIs	https://doi.org/10.1016/j.nahs.2009.04.007
Publication status	Published - 2009 Nov

Bibliographical note

Funding 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
Analysis
Computer Science Applications

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10.1016/j.nahs.2009.04.007

Cite this

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AU - Balachandran, K.

AU - Kim, J. H.

N1 - Funding 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.

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AB - 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.

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Exact null controllability of a semilinear parabolic equation arising in finance

Abstract

Bibliographical note

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