In this paper, we perform an a posteriori error analysis of a multiscale operator decomposition finite element method for the solution of a system of coupled elliptic problems. The goal is to compute accurate error estimates that account for the effects arising from multiscale discretization via operator decomposition. Our approach to error estimation is based on a well known a posteriori analy...

The purpose of this note is to study the existence a nontrivial solution for an elliptic system which comes from newly introduced mathematical problem so called Field-Road model. Specifically, it consists coupled equations set in domains different dimensions together with some interaction non classical type. We consider truncated by imposing Dirichlet boundary condi...

Models of two phase flows in porous media, used in petroleum engineering, lead to a system of two coupled equations with elliptic and parabolic degenerate terms, and two unknowns, the saturation and the pressure. For the purpose of their approximation, a coupled scheme, consisting in a finite volume method together with a phase-by-phase upstream weighting scheme, is used in the industrial setti...

this paper is concerned with the existence of multiple positive‎ ‎solutions for a quasilinear elliptic system involving concave-convex‎ ‎nonlinearities‎ ‎and sign-changing weight functions‎. ‎with the help of the nehari manifold and palais-smale condition‎, ‎we prove that the system has at least two nontrivial positive‎ ‎solutions‎, ‎when the pair of parameters $(lambda,mu)$ belongs to a certai...

Selection Algorithm and Generation Algorithm of elliptic curves have been the focus of research and hotspot of the Elliptic Curve Cryptosystem. This paper discusses a random elliptic curve realization method of Embedded Mobile Equipment, the SEA algorithm and its improved algorithm from Elliptic Curve's selection, Elliptic Curve's structure and Elliptic Curve's generation. Ensuring that the emb...

We study nonlinear asymptotic stability of small–amplitude Lax shocks in a model consisting of a system of multi–dimensional conservation laws coupled with an elliptic system. Such a model can be found in context of dynamics of a gas in presence of radiation. Our main result asserts that the standard uniform Evans stability condition implies nonlinear stability. The main analysis is based on th...

The evolution of a Bose–Einstein condensate (BEC) with an internal degree of freedom, i.e., spinor BEC, is governed by a system of three coupled mean-field equations. The system admits the application of the inverse scattering transform and Hirota bilinear method under appropriate conditions, which makes it possible to generate exact analytical solutions relevant to physical applications. Here,...

analysis of iterative substructuring algorithms for elliptic problems in three dimensions. Least-squares mixed-nite elements for second-order elliptic problems. A least-squares approach based on a discrete minus one inner product for rst order systems. Technical report, Brookhaven National Laboratory, 1994. 4] J. H. Bramble and J. E. Pasciak. Least-squares methods for Stokes equations based on ...

this paper addresses synchronizing two coupled chaotic fitzhugh–nagumo (fhn) neurons with weakly gap junction under external electrical stimulation (ees). to transmit information among coupled neurons, by generalization of the integer-order fhn equations of the coupled system into the fractional-order in frequency domain using crone approach, the behavior of each coupled neuron relies on its pa...