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On exact null controllability of Black-Scholes equation

Kumarasamy Sakthivel;  Krishnan Balachandran;  Rangarajan Sowrirajan;  Jeong-Hoon Kim — 2008

Kybernetika

In this paper we discuss the exact null controllability of linear as well as nonlinear Black–Scholes equation when both the stock volatility and risk-free interest rate influence the stock price but they are not known with certainty while the control is distributed over a subdomain. The proof of the linear problem relies on a Carleman estimate and observability inequality for its own dual problem and that of the nonlinear one relies on the infinite dimensional Kakutani fixed point theorem with L 2 ...

Null controllability of a nonlinear diffusion system in reactor dynamics

Kumarasamy Sakthivel;  Krishnan Balachandran;  Jong-Yeoul Park;  Ganeshan Devipriya — 2010

Kybernetika

In this paper, we prove the exact null controllability of certain diffusion system by rewriting it as an equivalent nonlinear parabolic integrodifferential equation with variable coefficients in a bounded interval of ℝ with a distributed control acting on a subinterval. We first prove a global null controllability result of an associated linearized integrodifferential equation by establishing a suitable observability estimate for adjoint system with appropriate assumptions on the coefficients. Then...

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