Herbert Egger, Michael Klibanov, Heinz Engl,
"Global uniqueness and Hölder stability for recovering a nonlinear source term in a parabolic equation"
, in Inverse Problems, Vol. 21, Seite(n) 271-290, 2005, ISSN: 0266-5611
Original Titel:
Global uniqueness and Hölder stability for recovering a nonlinear source term in a parabolic equation
Sprache des Titels:
Englisch
Original Kurzfassung:
Consider the semilinear parabolic equation
−u_t(x,t) + u_xx + q(u) = f (x,t),
with the initial condition
u(x,0) = u_0(x),
Dirichlet boundary conditions
u(0,t) = phi_0(t), u(1,t) = phi_1(t)
and a sufficiently regular source term q(·), which is assumed to be known a priori on the range of u_0(x). We investigate the inverse problem of determining the function q(·) outside this range from measurements of the
Neumann boundary data
u_x(0,t) = psi_0(t), u_x(1,t) = psi1(t).
Via the method of Carleman estimates,we derive global uniqueness of a solution (u,q) to this inverse problem and Hölder stability of the functions u and q with respect to errors in the Neumann data psi_0, psi_1, the initial condition u_0 and the a priori knowledge of the function q (on the range of u_0). The results are illustrated by numerical tests. The results of this paper can be extended to more general nonlinear parabolic equations.
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