Degenerate hyperbolic equations are approximated by uniformly hyperbolic ones to prove controllability in higher dimensions for the first time.
Cavalheiro, An approximation theorem for solutions of degenerate elliptic equations,Proc
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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.
Courant's nodal domain theorem and the residual nature of simple eigenvalues under perturbations both hold for the degenerate elliptic operator A = -div(w ∇·) with w > 0 inside Ω and w = 0 on part of ∂Ω.
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.
Shape design approximation proposed for degenerate PDEs, used to obtain Carleman estimates for null controllability of degenerate parabolic equations by avoiding second derivatives.
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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Some Key Properties of Eigenfunctions Linked to Degenerate Elliptic Differential Operators
Courant's nodal domain theorem and the residual nature of simple eigenvalues under perturbations both hold for the degenerate elliptic operator A = -div(w ∇·) with w > 0 inside Ω and w = 0 on part of ∂Ω.
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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.
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A Shape Design Approximation for Degenerate Partial Differential Equations and Its Application
Shape design approximation proposed for degenerate PDEs, used to obtain Carleman estimates for null controllability of degenerate parabolic equations by avoiding second derivatives.