6 research outputs found
Dissipative and non-dissipative evolutionary quasi-variational inequalities with gradient constraints
Evolutionary quasi-variational inequality (QVI) problems of dissipative and non-dissipative nature with pointwise constraints on the gradient are studied. A semi-discretization in time is employed for the study of the problems and the derivation of a numerical solution scheme, respectively. Convergence of the discretization procedure is proven and properties of the original infinite dimensional problem, such as existence, extra regularity and non-decrease in time, are derived. The proposed numerical solver reduces to a finite number of gradient-constrained convex optimization problems which can be solved rather efficiently. The paper ends with a report on numerical tests obtained by a variable splitting algorithm involving different nonlinearities and types of constraints
Parameter identification in a semilinear hyperbolic system
We consider the identification of a nonlinear friction law in a
one-dimensional damped wave equation from additional boundary measurements.
Well-posedness of the governing semilinear hyperbolic system is established via
semigroup theory and contraction arguments. We then investigte the inverse
problem of recovering the unknown nonlinear damping law from additional
boundary measurements of the pressure drop along the pipe. This coefficient
inverse problem is shown to be ill-posed and a variational regularization
method is considered for its stable solution. We prove existence of minimizers
for the Tikhonov functional and discuss the convergence of the regularized
solutions under an approximate source condition. The meaning of this condition
and some arguments for its validity are discussed in detail and numerical
results are presented for illustration of the theoretical findings
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Dissipative and non-dissipative evolutionary quasi-variational inequalities with gradient constraints
Evolutionary quasi-variational inequality (QVI) problems of dissipative
and non-dissipative nature with pointwise constraints on the gradient are
studied. A semi-discretization in time is employed for the study of the
problems and the derivation of a numerical solution scheme, respectively.
Convergence of the discretization procedure is proven and properties of the
original infinite dimensional problem, such as existence, extra regularity
and non-decrease in time, are derived. The proposed numerical solver reduces
to a finite number of gradient-constrained convex optimization problems which
can be solved rather efficiently. The paper ends with a report on numerical
tests obtained by a variable splitting algorithm involving different
nonlinearities and types of constraints