The paper addresses existence, uniqueness and approximation methods for a certain class of nonlinear parabolic quasi-variational inequality (QVI) problems with special gradient-type constraints. Problems of this nature are common in the mathematical modeling of superconductors and ionization in electrostatics. The results are developed based on monotone operator theory , C 0 semigroup methods a...

We consider an approximation scheme for systems of linear delay-differential equations of neutral type. The finite dimensional approximating systems are constructed with basis functions defined using linear splines, extending to neutral equations a scheme which had previously been defined only for retarded equations. A Trotter-Kato semigroup convergence result is proved, and numerical results a...

We call (T (t))t≥0 an abstract delay semigroup. This notion is introduced in more detail in Section 2. The semigroup thus obtained is rarely a contraction semigroup. In this paper we will show that under very mild conditions, we may change the inner product on E into an equivalent inner product, such that the delay semigroup becomes a (generalized) contraction semigroup. A contraction semigroup...

Left-discrimination of a semigroup is defined and shown to be a sufficient condition that a semigroup be isomorphic to the input semigroup of its semigroup automaton, a necessary condition if the semigroup is finite. The left-discrimination sequence of an automaton is defined as a sequence of semigroups beginning with the input semigroup of the automaton, each member being the input semigroup o...

We present a polynomial-time reduction of the discrete logarithm problem in any periodic (a.k.a. torsion) semigroup (Semigroup DLP) to the classic DLP in a subgroup of the same semigroup. It follows that Semigroup DLP can be solved in polynomial time by quantum computers, and that Semigroup DLP has subexponential algorithms whenever the classic DLP in the corresponding groups has subexponential...

This paper is concerned with the eigenvalue decay of the solution to operator Lya-punov equations with right-hand sides of finite rank. We show that the kth eigenvalue decays exponentially in √ k, provided that the involved operator A generates an exponentially stable continuous semigroup, and A is either self-adjoint or diagonalizable. Numerical experiments with discretizations of 1D and 2D PD...

The paper serves as a review on the basic results showing how functional analytic tools have been applied in numerical analysis. It deals with abstract Cauchy problems and present how their solutions are approximated by using space and time discretisations. To this end we introduce and apply the basic notions of operator semigroup theory. The convergence is analysed through the famous theorems ...

In [BMV03]and [Bre02] the authors proposed to compute the characteristic roots of Delay Differential Equations (DDEs) with multiple discrete and distributed delays by approximating the derivative in the infinitesimal generator of the solution operator semigroup by Runge-Kutta (RK) and Linear Multistep (LMS) methods, respectively. In this work the same approach is proposed in a new version based...