Continuous dependence of solutions for ill-posed evolution problems.
Matthew A. Fury, Rhonda Jo Hughes · DOAJ (DOAJ: Directory of Open Access Journals) · 2010
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 $$displaylines{ frac{du(t)}{dt} = A(t,D)u(t) quad 0leq t<T cr u(0) = chi. }$$ We determine functions $f:[0,T]imes [0,infty)o mathbb{R}$ for which solutions of the well-posed problem $$displaylines{ frac{dv(t)}{dt} = f(t,D)v(t) quad 0leq t