Carleman estimates for degenerate parabolic operators with applications to null controllability View Full Text


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Article Info

DATE

2006-05

AUTHORS

F. Alabau-Boussouira, P. Cannarsa, G. Fragnelli

ABSTRACT

We prove an estimate of Carleman type for the one dimensional heat equation $$ u_t - \left( {a\left( x \right)u_x } \right)_x + c\left( {t,x} \right)u = h\left( {t,x} \right),\quad \left( {t,x} \right) \in \left( {0,T} \right) \times \left( {0,1} \right), $$ where a(·) is degenerate at 0. Such an estimate is derived for a special pseudo-convex weight function related to the degeneracy rate of a(·). Then, we study the null controllability on [0, 1] of the semilinear degenerate parabolic equation $$ u_t - \left( {a\left( x \right)u_x } \right)_x + f\left( {t,x,u} \right) = h\left( {t,x} \right)\chi _\omega \left( x \right), $$ where (t, x) ∈(0, T) × (0, 1), ω=(α, β) ⊂⊂ [0, 1], and f is locally Lipschitz with respect to u. More... »

PAGES

161-204

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00028-006-0222-6

DOI

http://dx.doi.org/10.1007/s00028-006-0222-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1013053088


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