Eighth Mississippi State - UAB Conference on Differential Equations and
Computational Simulations.
Electron. J. Diff. Eqns., Conference 19 (2010), pp. 37-44.
Title: Quasireversibility for inhomogeneous ill-posed problems
in Hilbert spaces
Author: Beth M. Campbell Hetrick (Gettysburg College, PA, USA)
Abstract:
In a Hilbert space $\mathcal{H}$, the inhomogeneous ill-posed
abstract Cauchy problem is given by
$\frac{du}{dt} = Au(t) + h(t)$, $u(0) = \chi$,
$0 \leq t < T$; where $A$ is a positive self-adjoint linear
operator acting on $\mathcal{H}$, $\chi \in \mathcal{H}$,
and $h: [0,T) \to \mathcal{H}$. Using semigroup theory,
we obtain Holder continuous dependence for the control
problem generated by the method of quasireversibility.
Published September 25, 2010.
Math Subject Classifications: 47A52, 35R25, 35A35.
Key Words: Quasireversibility; ill-posed problems.