The paper is concerned with the finite-time stabilization of a coupled PDE–ODE system describing motion an overhead crane flexible cable. dynamics cable described by wave equation variable coefficient which affine function curvilinear abscissa along Using several changes variables, backstepping transformation, and stable second-order ODE for conveniently chosen variable, we prove that global oc...

Current spectral simulations of Einstein’s equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudospectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on ...

We apply a multiple–time version of the reductive perturbation method to study long waves as governed by the Boussinesq model equation. By requiring the absence of secular producing terms in each order of the perturbative scheme, we show that the solitary–wave of the Boussinesq equation can be written as a solitary–wave satisfying simultaneously all equations of the KdV hierarchy, each one in a...

Presently there is a little information that relates to heat shield systems.  Also this information is not certain in so many cases.  The main reason is that accurate calculations for measuring the sacrificing rate of various materials have not been obtained yet.  Additionally, the real scale test has two disadvantages: high cost and low flexibility, and for each case we must perform a new test...

In this article, we have presented a peristaltic flow of third order fluid in a channel with variable viscosity. The governing equations are constructed under long wave length and low Reynolds number approximations. A regular perturbation technique is applied and obtained expressions for the stream function, temperature, and concentration at a small Deborah number. The pertinent features of var...

We report the developments of hydrodynamic instabilities in several wellbalanced finite volume schemes that are observed during the computation of the temporal evolution of an out-balance flow which is essentially a kinematic wave. The numerical simulations are based on the one-dimensional shallow-water equations for a uniformly sloping bed with hydraulic resistance. Subsequently, we highlight ...

This paper discusses the existence and stability of solitary-wave solutions of a general higher-order Benjamin-Bona-Mahony (BBM) equation, which involves pseudo-differential operators for the linear part. One of such equations can be derived from water-wave problems as second-order approximate equations from fully nonlinear governing equations. Under some conditions on the symbols of pseudo-dif...

the aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. the state and co-state are approximated by the lowest order raviart-thomas mixed finite element spaces and the control is not discreted. optimal error estimates in l2 are established for the state...