is considered. We are interesting for asymptotics of the perturbed solution u(x, t; ε) as ε→ 0. Perturbation theory for integrable equations remains a very attractive task. As a rule a perturbation of smooth solutions such as a single soliton were usually considered. We intend here to discuss a perturbation of a singular solution under assumption that the perturbed solution has singularities as...

This paper concerned with a model reduction of infinite dimensional systems by using the singular perturbation approximation. The system considered is that of the exponentially stable linear system with bounded and finite-rank input and output operators such that the balanced realization can be performed on the system. Furthermore, the singular perturbation method is applied to reduce the order...

Analytic approximations of the time-evolution of the single enzyme-substrate reaction are valid for all but a small region of parameter spsce in the positive initial enzyme-initial substrate concentration plane. We find velocity equations for the substrate decomposition and product formation with the aid of the total quasi-steady-state approximation and an aggregation technique for cases where ...

Poisson-Nernst-Planck (PNP) systems are considered in the case of vanishing permanent charge. A detailed case study, based on natural categories described by system boundary conditions and flux, is carried out via simulation and singular perturbation analysis. Our results confirm the rich structure inherent in these systems. A natural quantity, the quotient of the Debye and characteristic lengt...

Privacy of information and security issues now-a-days has become the requisite because of big data. A novel framework for extracting and deriving information when the data is distributed amongst the multiple parties is presented by Privacy Preserving Data Mining (PPDM). The concern of PPDM system is to protect the disclosure of information and its misuse. Major issue with PPDM that exists is to...

We show that stationary statistical properties for uniformly dissipative dynamical systems are upper semi-continuous under regular perturbation and a special type of singular perturbation in time of relaxation type. The results presented are applicable to many physical systems such as the singular limit of infinite Prandtl-Darcy number in the Darcy-Boussinesq system for convection in porous med...

A singularly perturbed model is proposed for a system comprised of a PEM Fuel Cell(PEM-FC) with Natural Gas Hydrogen Reformer (NG-HR). This eighteenth order system is decomposedinto slow and fast lower order subsystems using singular perturbation techniques that provides tools forseparation and order reduction. Then, three different types of controllers, namely an optimal full-order,a near-opti...

To solve a stochastic linear evolution equation numerically, nite dimensional approximations are commonly used. For a good approximation, one might end up with a sequence of ordinary stochastic linear equations of high order. To reduce the high dimension for practical computations, we consider the singular perturbation approximation as a model order reduction technique in this paper. This appro...

In this paper we study the singular perturbation of ∫ (1−|∇u|2)2 by ε2|∇2u|2. This problem, which could be thought as the natural second order version of the classical singular perturbation of the potential energy ∫ (1 − u2)2 by ε2|∇u|2, leads, as in the first order case, to energy concentration effects on hypersurfaces. In the two dimensional case we study the natural domain for the limiting e...

It is well known that the standard finite element method based on the space Vh of continuous piecewise linear functions is not reliable in solving singular perturbation problems. It is also known that the solution of a two-point boundary-value singular perturbation problem admits a decomposition into a regular part and a finite linear combination of explicit singular functions. Taking into acco...