52 research outputs found
Heuristic parameter-choice rules for convex variational regularization based on error estimates
In this paper, we are interested in heuristic parameter choice rules for
general convex variational regularization which are based on error estimates.
Two such rules are derived and generalize those from quadratic regularization,
namely the Hanke-Raus rule and quasi-optimality criterion. A posteriori error
estimates are shown for the Hanke-Raus rule, and convergence for both rules is
also discussed. Numerical results for both rules are presented to illustrate
their applicability
Regularity of a inverse problem for generic parabolic equations
The paper studies some inverse boundary value problem for simplest parabolic
equations such that the homogenuous Cauchy condition is ill posed at initial
time. Some regularity of the solution is established for a wide class of
boundary value inputs.Comment: 9 page
On prescribed change of profile for solutions of parabolic equations
Parabolic equations with homogeneous Dirichlet conditions on the boundary are
studied in a setting where the solutions are required to have a prescribed
change of the profile in fixed time, instead of a Cauchy condition. It is shown
that this problem is well-posed in L_2-setting. Existence and regularity
results are established, as well as an analog of the maximum principle
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