Time: 9h30, Tuesday, November 21, 2017
Location: Room 4, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi

Abstract: Let $H$ be a Hilbert space with the inner product $$ and the norm $|cdot|$, $A(t)$ a positive self-adjoint unbounded time-dependent operator on $H$ and $varepsilon > 0$. We establish stability estimates of H"older type and propose a regularization method with error estimates of H"older type for the ill-posed backward semi-linear parabolic equation

$$

begin{cases} u_t(t)+ A(t)u(t)=f(t,u(t)), quad 0 < tleqslant T,

|u(T)-varphi|leqslantvarepsilon,

end{cases}

$$

with the source function $f$ satisfying a local Lipschitz condition.

This is a joint work with Nguyen Van Duc and Nguyen Van Thang.