In this paper, we consider a seventh-order generalized Korteweg–de Vries (GKdV) equation and study the boundary stability results concerning the inverse problem of recovering a space-dependent source term. We establish a new boundary Carleman estimate for the seventh-order linear operator with the Dirichlet–Neumann type boundary conditions. Using this crucial estimate along with regularity result of the nonlinear GKdV equation, we establish a Lipschitz stability estimate of GKdV equation.

中文翻译：

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广义Korteweg-de Vries方程的反源问题

在本文中，我们考虑了七阶广义Korteweg-de Vries（GKdV）方程，并研究了关于恢复空间相关源项的反问题的边界稳定性结果。我们用Dirichlet-Neumann型边界条件为七阶线性算子建立了新的边界Carleman估计。使用该关键估计以及非线性GKdV方程的正则结果，我们建立了GKdV方程的Lipschitz稳定性估计。