Eighth Mississippi State - UAB Conference on Differential Equations and
Computational Simulations.
Electron. J. Diff. Eqns., Conference 19 (2010), pp. 99-121.
Title: Continuous dependence of solutions for ill-posed evolution problems
Authors: Matthew Fury (Bryn Mawr College, PA, USA)
Rhonda J. Hughes (Bryn Mawr College, PA, USA)
Abstract:
We prove Holder-continuous dependence results for the difference
between certain ill-posed and well-posed evolution problems in
a Hilbert space. Specifically, given a positive self-adjoint
operator D in a Hilbert space, we consider the ill-posed evolution
problem
$$\displaylines{
\frac{du(t)}{dt} = A(t,D)u(t) \quad 0\leq t