Establishes L2 boundary trace regularity and large-time observability with interior remainder for boundary-degenerate hyperbolic equations with α<1, plus a logarithmic-loss obstruction at the critical value α=1.
Evans,Partial Differential Equations, American Mathematical Society, New York
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Extends separable variable method to obtain Lebeau-Robbiano spectral inequality and null controllability for a distinct degenerate parabolic equation with measurable-set internal control.
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.
citing papers explorer
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Hidden Boundary Trace Regularity and an Observability Estimate with Interior Remainder for Boundary-Degenerate Hyperbolic Equations
Establishes L2 boundary trace regularity and large-time observability with interior remainder for boundary-degenerate hyperbolic equations with α<1, plus a logarithmic-loss obstruction at the critical value α=1.
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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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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.