Carleman estimates for semi-discrete parabolic operators with a discontinuous diffusion coefficient and application to controllability

2012/11/09 by Nguyen, Thuy
#Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1211.2061

Abstract

In the discrete setting of one-dimensional finite-differences we prove a Carleman estimate for a semi-discretization of the parabolic operator ∂_t-∂_x (c∂_x) where the diffusion coefficient c has a jump. As a consequence of this Carleman estimate, we deduce consistent null-controllability results for classes of semi-linear parabolic equations.

Related

• Carleman estimates and controllability results for fully-discrete\n approximations of 1-D parabolic equations
• Carleman estimate for semi-discrete stochastic parabolic operators in arbitrary dimension and applications to controllability
• Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions
• Null controllability for stochastic semi-discrete parabolic equations
• Carleman Estimates for Parabolic Operators with Discontinuous and Anisotropic Diffusion Coefficients, an Elementary Approach