有界区域上具有混合边界条件的Korteweg-de Vries-Burgers方程轨迹的局部精确能控性
Local Exact Controllability to the Trajectories of the Korteweg-de Vries-Burgers Equation on a Bounded Domain with Mixed Boundary Conditions
摘要：
研究了有界区域上Korteweg-de Vries-Burgers（KDVB）方程的内部控制问题.扩散系数与时间有关，边界条件是混合的，在这个意义上，齐次Dirichlet和周期性Neumann边界条件被认为是。利用对偶性和新的Carleman估计，证明了线性化系统轨迹的精确能控性。然后，利用反演定理，我们推导出原KdVB方程，这是非线性的轨迹的局部精确能控性。
英文摘要：
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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