LIPSCHITZ STABILITY IN INVERSE PARABOLIC PROBLEMS BY THE CARLEMAN ESTIMATE

Citation
Oy. Imanuvilov et M. Yamamoto, LIPSCHITZ STABILITY IN INVERSE PARABOLIC PROBLEMS BY THE CARLEMAN ESTIMATE, Inverse problems (Print), 14(5), 1998, pp. 1229-1245
Citations number
24
Categorie Soggetti
Mathematics,"Physycs, Mathematical","Physycs, Mathematical",Mathematics
Journal title
ISSN journal
02665611
Volume
14
Issue
5
Year of publication
1998
Pages
1229 - 1245
Database
ISI
SICI code
0266-5611(1998)14:5<1229:LSIIPP>2.0.ZU;2-8
Abstract
We consider a system yt(t, x) = -Ay(t, x) + g(t, x) 0 < t < T, x epsil on Omega y(theta, x) = y(0)(x) x epsilon Omega with a suitable boundar y condition, where Omega subset of R-n is a bounded domain, -A is a un iformly elliptic operator of the second order whose coefficients are s uitably regular for (t, x), theta epsilon]0, T[ is fixed, and a functi on g(t, x) satisfies \gt(t, x)\ less than or equal to C\g(theta, x) \ for (t, x) epsilon [0, T] x <(Omega)over bar>. Our inverse problems ar e determinations of g using overdetermining data gamma(vertical bar]0, T[x omega) or {gamma(vertical bar]0, T[x Gamma 0), del gamma(vertical bar]0, T[x Gamma 0)}, where omega subset of Omega and Gamma(0) subset of partial derivative Omega. Our main result is the Lipschitz stabilit y in these inverse problems. We also consider the determination of f = f(x), x epsilon Omega in the case of g(t, x) = f(x)R(t, x) with given R satisfying R(theta, .) > 0 on Omega. Finally, we discuss an upper e stimation of our overdetermining data by means of f.