Degenerate hyperbolic equations are approximated by uniformly hyperbolic ones to prove controllability in higher dimensions for the first time.
Lions, Exact controllability, stabilizability and perturbations for distributed systems, SIAM Rev., 30(1988), 1-68
4 Pith papers cite this work. Polarity classification is still indexing.
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Null controllability is established for a multi-dimensional degenerate parabolic PDE with an interior degenerate point outside the control domain by approximating the system with uniformly elliptic equations and using Carleman estimates to obtain observability.
Extends separable variable method to obtain Lebeau-Robbiano spectral inequality and null controllability for a distinct degenerate parabolic equation with measurable-set internal control.
Proves well-posedness of degenerate parabolic PDEs with Dirichlet conditions, develops shape-design approximation by non-degenerate equations, and obtains boundary observability inequality as application.
citing papers explorer
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Approximation of Degenerate Hyperbolic Equations with Interior Degeneracy and Applications to Controllability
Degenerate hyperbolic equations are approximated by uniformly hyperbolic ones to prove controllability in higher dimensions for the first time.
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Null Controllability for a Multi-Dimensional Degenerate Parabolic Equation with Degenerated Interior Point
Null controllability is established for a multi-dimensional degenerate parabolic PDE with an interior degenerate point outside the control domain by approximating the system with uniformly elliptic equations and using Carleman estimates to obtain observability.
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Null Controllability for Degenerate Parabolic Equations with Internal Control Applied on a Measurable Subset
Extends separable variable method to obtain Lebeau-Robbiano spectral inequality and null controllability for a distinct degenerate parabolic equation with measurable-set internal control.
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Shape Design for Degenerate Parabolic Equations with Degenerate Boundaries and Its Application to Boundary Observability
Proves well-posedness of degenerate parabolic PDEs with Dirichlet conditions, develops shape-design approximation by non-degenerate equations, and obtains boundary observability inequality as application.