Abstract. In this paper we study the Borel summability of formal solutions with a parameter of first order semilinear system of partial differential equations with n independent variables. In [Singular perturbation of linear systems with a regular singularity, J. Dynam. Control. Syst. 8 (2002), 313–322], Balser and Kostov proved the Borel summability of formal solutions with respect to a singul...

is obtained as another special case' In this paper, we formulate continuous time linear fractional shift invariant (LFSI) systems that generalize the well-known linear time invariant (LTI) systems by means of an angle parameter 4. LTI systems are obtained as a special case of LFSl systems for 4 = 0. LFSl systems belong to the large class of time-varying systems. Whereas LTI systems commute with...

The main focus of this paper is on an a-posteriori analysis for different model-order strategies applied to optimal control problems governed by linear parabolic partial differential equations. Based on a perturbation method it is deduced how far the suboptimal control, computed on the basis of the reduced-order model, is from the (unknown) exact one. For the model-order reduction, H2,α-norm op...

in this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. a fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. thomas algorithm is used to solve the tri-diagonal system. the stability of the algorithm is investigated. it ...

The reduced 1D Poisson-Nernst-Planck (PNP) model of artificial nanopores in the presence of a permanent charge on the channel wall is studied. More specifically, we consider the limit where the channel length exceed much the Debye screening length and channel’s charge is sufficiently small. Ion transport is described by the nonequillibrium steady-state solution of the PNP system within a singul...

Ionic channels and semiconductor devices use atomic scale structures to control macroscopic flows from one reservoir to another. The onedimensional steady-state Poisson-Nernst-Planck (PNP) system is a useful representation of these devices but experience shows that describing the reservoirs as boundary conditions is difficult. We study the PNP system for two types of ions with three regions of ...

Introduction This extended abstract summarizes a methodology along with the experimental results to adaptively reduce timevarying lateral tape motion (LTM) in a Linear Tape-Open (LTO) drive. For the adaptive regulation, the LTO actuator dynamics is modeled with a Linear Time Invariant (LTI) model and control of time-varying LTM disturbances is done via an adaptable linear feedback controller. A...

The reduced 1D Poisson-Nernst-Planck (PNP) model of artificial nanopores in the presence of a permanent charge on the channel wall is studied. More specifically, we consider the limit where the channel length exceed much the Debye screening length and channel’s charge is sufficiently small. Ion transport is described by the nonequillibrium steady-state solution of the PNP system within a singul...

When we apply the steady-state approximation (SSA) in chemical kinetics, we typically argue that some of the intermediates are highly reactive, so that they are removed as fast as they are made. We then set the corresponding rates of change to zero. What we are saying is not that these rates are identically zero, of course, but that they are much smaller than the other rates of reaction. The st...

A singularly perturbed system for doubly diffusive convection equations, called the artificial compressible system, is considered on a two-dimensional infinite layer parameters range where Hopf bifurcation occurs in corresponding incompressible system. The spectrum of linearized operator time periodic function space investigated detail near point when singular perturbation parameter small. resu...