A REGULARIZATION METHOD FOR BACKWARD PARABOLIC EQUATIONS WITH TIME-DEPENDENT COEFFICIENTS

Tóm tắt

Let H be a Hilbert space with the norm k · k and A(t);(0 6 t 6 T)
be positive self-adjoint unbounded operators from D(A(t)) ⊂ H to H. In the
paper, we propose a regularization method for the ill-posed backward parabolic
equation with time-dependent coefficients
(u ku t (+ TA ) - (t)fuk= 0 6 "; f ; 0 < t < T; 2 H; " > 0:
A priori and a posteriori parameter choice rules are suggested which yield errors
estimates of H¨older type. Our errors estimates improve the related results in [4]