We study here the convergence of a finite volume scheme for a coupled system of an hyperbolic and an elliptic equations defined on an open bounded set of IR. On the elliptic equation, a four points finite volume scheme is used then an error estimate on a discrete H norm of order h is proved, where h defines the size of the triangulation. On the hyperbolic equation, one uses an upstream scheme w...

We analyze a diffuse interface type approximation, known as the diffuse domain approach, of a linear coupled bulk-surface elliptic PDE system. The well-posedness of the diffuse domain approximation is shown using weighted Sobolev spaces and we prove that the solution to the diffuse domain approximation converges weakly to the solution of the coupled bulk-surface elliptic system as the approxima...

In recent years it has been trying that with regard to the question of computational complexity of discrete logarithm more strength and less in the elliptic curve than other hard issues, applications such as elliptic curve cryptography, a blind  digital signature method, other methods such as encryption replacement DLP. In this paper, a new blind digital signature scheme based on elliptic curve...

We obtain an elliptic system of monopole equations on 8-manifolds with Spin(7) holonomy by minimizing an action involving negative spinors coupled to an Abelian gauge field.

In the paper, with the aid of symbolic computation, we investigate the generalized Hirota–Satsuma coupled KdV system via our Weierstrass semi-rational expansion method presented recently using the rational expansion of Weierstrass elliptic function and its first-order derivative. As a consequence, three families of newWeierstrass elliptic function solutions via Weierstrass elliptic function }(n...

We study the convergence of two coupled numerical schemes, which are a discretization of a so-called elliptic-hyperbolic system. Only weak convergence properties are proved on the discrete diffusion of the elliptic problem and an adaptation of the H-convergence method gives a convergence property of the elliptic part of the scheme. The limit of the approximate solution is then the solution of a...

The coupled Kadomtsev–Petviashvili system associated with an elliptic curve, proposed by Date, Jimbo, and Miwa [J. Phys. Soc. Jpn., 52:766–771, 1983], is reinvestigated within the direct linearization framework, which provides us more insights into integrability of this model from perspective a general linear integral equation. As result, we successfully construct for not only Lax pair composed...

The numerical solution of a model describing a two-dimensional fluidized bed by a Chebyshev super spectral viscosity (SSV) method is considered. The model is in the form of a hyperbolic system of conservation laws with a source term, coupled with an elliptic equation for determining a stream function. The coupled elliptic equation is solved by a finite difference method. The mixed SSV/finite di...

the aim of the paper is to analyze electro-thermo nonlinear vibration of a double-piezoelectric composite microplate-system (dpcmps) based on nonlocal piezoelasticity theory. the two microplates are assumed to be connected by an enclosing elastic medium which is simulated by pasternak foundation. both of smart composite microplates are made of poly-vinylidene fluoride (pvdf) reinforced by zigza...

This paper is concerned with the state-constrained optimal control of the twodimensional thermistor problem, a quasi-linear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Existence, uniqueness and continuity for the state system are derived by employing maximal elliptic and parabo...