Найдено научных статей и публикаций: 2, для научной тематики: Carleman estimates
1.
K.Sakthivel, G.Devipriya, K.Balachandran, J.-H.Kim
- Numerical Functional Analysis and Optimization , 2010
This article establishes the controllability to the trajectories of a reaction-diffusion-advection
system describing predator–prey model by using distributed controls acting on a single equation
with the no-flux boundary conditions. We first prove the exact null controllability of an
associated linear...
This article establishes the controllability to the trajectories of a reaction-diffusion-advection
system describing predator–prey model by using distributed controls acting on a single equation
with the no-flux boundary conditions. We first prove the exact null controllability of an
associated linearized problem by establishing an observability estimate, derived from a global
Carleman type inequality, for the adjoint system. The proof of the nonlinear problem relies on
the suitable regularity of the control and Kakutani’s fixed point theorem.
2.
K. Sakthivel, G. Devipriya, K. Balachandran and J.-H. Kim
- nonlinear analysis- hybrid systems , 2009
This paper is concerned with the exact null controllability of certain semilinear Black–Scholes type equations in a bounded interval of 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 l...
This paper is concerned with the exact null controllability of certain semilinear Black–Scholes type equations in a bounded interval of 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.