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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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.
A quantitative weak unique continuation theorem is established for backward degenerate parabolic equations on annular domains with degenerate interior points by approximating with non-degenerate equations and applying Carleman estimates.
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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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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Quantitative Weak Unique Continuation on Annular Domains for Backward Degenerate Parabolic Equations with Degenerate Interior Points
A quantitative weak unique continuation theorem is established for backward degenerate parabolic equations on annular domains with degenerate interior points by approximating with non-degenerate equations and applying Carleman estimates.
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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.