2019/02/28 by Eduardo Cerpa, Cristhian Montoya, Bingyu Zhang +1 · 17 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Applied mathematics #Boundary (topology) #Boundary value problem #Bounded function #Burgers' equation #Controllability #Dirichlet boundary condition #Domain (mathematical analysis) #Korteweg–de Vries equation #Mathematical analysis #Mathematics #Neumann boundary condition #Nonlinear system #Numerical methods for differential equations #Partial differential equation #Stability and Controllability of Differential Equations #math.OC
paper · pdf · doi:10.1016/j.jde.2019.10.043
published in Journal of Differential Equations 268(9), 4945-4972 (Elsevier BV)
arxiv created 2019/02/28 · openalex created_date 2019/03/02 · openalex publication_date 2019/11/06 · arxiv updated 2020/02/03 · openalex updated_date 2026/08/05
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.