Unique continuation and approximate controllability for a degenerate parabolic equation

Details Unique continuation and approximate controllability for a degenerate parabolic equation Unique continuation and approximate controllability for a degenerate parabolic equation

2011-07-16

arxiv.org/abs/1107.3246v3

Mathematics

Analysis of PDEs

for the special issue of Applicable Analysis on PDE and Inverse Problems (Guest Editors: R. Triggiani, A. Favini and A. Lorenz

Scientific paper

This paper studies unique continuation for weakly degenerate parabolic equations in one space dimension. A new Carleman estimate of local type is obtained to deduce that all solutions that vanish on the degeneracy set, together with their conormal derivative, are identically equal to zero. An approximate controllability result for weakly degenerate parabolic equations under Dirichlet boundary condition is deduced.

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