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arXiv · 1902.11270

Local Exact Controllability to the Trajectories of the Korteweg-de Vries-Burgers Equation on a Bounded Domain with Mixed Boundary Conditions

Eduardo Cerpa·Cristhian Montoya·Bingyu Zhang
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Abstract

This paper studies the internal control of the Korteweg-de Vries-Burgers (KdVB) equation on a bounded domain. The diffusion coefficient is time-dependent and the boundary conditions are mixed in the sense that homogeneous Dirichlet and periodic Neumann boundary conditions are considered. The exact controllability to the trajectories is proven for a linearized system by using duality and getting a new Carleman estimate. Then, using an inversion theorem we deduce the local exact controllability to the trajectories for the original KdVB equation, which is nonlinear.

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Eduardo Cerpa, Cristhian Montoya, Bingyu Zhang. 2019-02-28. Local Exact Controllability to the Trajectories of the Korteweg-de Vries-Burgers Equation on a Bounded Domain with Mixed Boundary Conditions. https://doi.org/10.1016/j.jde.2019.10.043

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