Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 19 (2010), pp. 37-44.

Quasireversibility for inhomogeneous ill-posed problems in Hilbert spaces

Beth M. Campbell Hetrick

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.

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Beth M. Campbell Hetrick
Department of Mathematics, Gettysburg College
Gettysburg, PA 17325, USA
email: bcampbel@gettysburg.edu

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