http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/135982This work is interested in the study of the passage of a long gravity wave above an immersed vertical barrier. The latter is placed at a right angle in the middle of the occupied fluid domain which is limited vertically by both a free surface and an impermeable horizontal bottom. We want to determine the field velocity and the local disturbances in the vicinity of the barrier. For this, we use the generalized theory of shallow water and complex variables method. For illustration, we consider a solitary wave as an emitted long wave.Laouar Abdelhamid and Guerziz Allaoua© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/267454The least-squares finite element method (LSFEM) has received increasing attention in recent years due to advantages over the Galerkin finite element method (GFEM). The method leads to a minimization problem in the L2-norm and thus results in a symmetric and positive definite matrix, even for first-order differential equations. In addition, the method contains an implicit streamline upwinding mechanism that prevents the appearance of oscillations that are characteristic of the Galerkin method. Thus, the least-squares approach does not require explicit stabilization and the associated stabilization parameters required by the Galerkin method. A new approach, the bubble enriched least-squares finite element method (BELSFEM), is presented and compared with the classical LSFEM. The BELSFEM requires a space-time element formulation and employs bubble functions in space and time to increase the accuracy of the finite element solution without degrading computational performance. We apply the BELSFEM and classical least-squares finite element methods to benchmark problems for 1D and 2D linear transport. The accuracy and performance are compared.Rajeev Kumar and Brian H. Dennis© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/816787The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopy analysis method (HAM). The continuous solution for the nonlinear system is given, which provides a convenient and straightforward approach to calculate the dynamics of the system. The HAM continuous solution generated by polynomial base functions is of comparable accuracy to the purely numerical fourth-order Runge-Kutta method. The convergence theorem for the three-dimensional case is also given.A. Sami Bataineh, M. S. M. Noorani, and I. Hashim© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/243459The homotopy analysis method (HAM) is applied to obtain the approximate traveling wave solutions of the coupled Whitham-Broer-Kaup (WBK) equations in shallow water. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the systems of nonlinear partial differential equations.M. M. Rashidi, D. D. Ganji, and S. Dinarvand© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/745242A new approach for demonstrating the global stability of ordinary differential equations is given. It is shown that if the curvature of solutions is bounded on some set, then any nonconstant orbits that remain in the set, must contain points that lie some minimum distance apart from each other. This is used to establish a negative-criterion for periodic orbits. This is extended to give a method of proving an equilibrium to be globally stable. The approach can also be used to rule out the sudden appearance of large-amplitude periodic orbits.C. Connell McCluskey© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/19529We implement a relatively new analytical technique, the variational iteration decomposition method (VIDM), for solving the eighth-order boundary value problems. The proposed method is an elegant combination of variational iteration method and decomposition method. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Numerical work is given to check the efficiency of the method. Comparisons are made to confirm the reliability and accuracy of the technique. The technique can be used as an alternative for solving nonlinear boundary value problems.Muhammad Aslam Noor and Syed Tauseef Mohyud-Din© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/49251We study the first-order nonhomogenous wave equation. We extend the convolution theorem into a general case with a double convolution as the nonhomogenous term. The uniqueness and continuity of the solution are proved and we provide some examples in order to validate our results.Adem Kılıçman and Hassan Eltayeb© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/18735In the present work, we consider a class of nonlinear optimal control problems, which can be called “optimal control problems in mechanics.” We deal with control systems whose dynamics can be described by a system of Euler-Lagrange or Hamilton equations. Using the variational structure of the solution of the corresponding boundary-value problems, we reduce the initial optimal control problem to an auxiliary problem of multiobjective programming. This technique makes it possible to apply some consistent numerical approximations of a multiobjective optimization problem to the initial optimal control problem. For solving the auxiliary problem, we propose an implementable numerical algorithm.Vadim Azhmyakov© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/19685This paper studies the existence of global solutions to the initial-boundary value problem for some nonlinear degenerate wave equations by means of compactness method and the potential well idea. Meanwhile, we investigate the decay estimate of the energy of the global solutions to this problem by using a difference inequality.Yaojun Ye© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/48527The stochastic finite element method (SFEM) is employed for solving stochastic one-dimension time-dependent differential equations with random coefficients. SFEM is used to have a fixed form of linear algebraic equations for polynomial chaos coefficients of the solution process. Four fixed forms are obtained in the cases of stochastic heat equation with stochastic heat capacity or heat conductivity coefficients and stochastic wave equation with stochastic mass density or elastic modulus coefficients. The relation between the exact deterministic solution and the mean of solution process is numerically studied.M. M. Saleh, I. L. El-Kalla, and M. M. Ehab© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/87696This paper investigates the local existence of the nonnegative solution and the finite time blow-up of solutions and boundary layer profiles of diffusion equations with nonlocal reaction sources; we also study the global existence and that the rate of blow-up is uniform in all compact subsets of the domain, the blow-up rate of |u(t)|∞ is precisely determined.Zhoujin Cui and Zuodong Yang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/49157The paper presents models of car dynamics with varying complexity. Joint coordinates and homogenous transformations are used to model the motion of a car. Having formulated the models of the car, we discuss the influence of the complexity of the model on numerical efficiency of integrating the equations describing car dynamics. Methods with both constant and adaptive step size have been applied. The results of numerical calculations are presented and conclusions are formulated.Marek Szczotka, Szymon Tengler, and Stanislaw Wojciech© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DENM/2006/32675A perturbation-theoretic analysis of rectifier circuits is presented. The governing differential equation of the half-wave rectifier with capacitor filter is analyzed by expanding the output voltage as a Taylor series with respect to an artificially introduced parameter in the nonlinearity of the diode characteristic as is done in quantum theory. The perturbation parameter introduced in the analysis is independent of the circuit components as compared to the method presented by multiple scales. The various terms appearing in the perturbation series are then modeled in the form of an equivalent circuit. This model is subsequently used in the analysis of full-wave rectifier. Matlab simulation results are included which confirm the validity of the theoretical formulations. Perturbation analysis acts a helpful tool in analyzing time-varying systems and chaotic systems.Vipin B. Vats and H. Parthasarathy© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DENM/2006/31797We present a finite volume discretization of the nonlinear elliptic problems. The discretization results in a nonlinear algebraic system of equations. A Newton-Krylov algorithm is also presented for solving the system of nonlinear algebraic equations. Numerically solving nonlinear partial differential equations consists of discretizing the nonlinear partial differential equation and then solving the formed nonlinear system of equations. We demonstrate the convergence of the discretization scheme and also the convergence of the Newton solver through a variety of practical numerical examples.Sanjay Kumar Khattri© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DENM/2006/52765The steady flow of an incompressible electrically conducting fluid over a semi-infinite moving vertical cylinder in the presence of a uniform transverse magnetic field is analyzed. The partial differential equations governing the flow are reduced to an ordinary differential equation, using the self-similarity transformation. The analysis deals with the existence of an exact solution to the boundary value problem by a shooting method.Maryem Amkadni and Adnane Azzouzi© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DENM/2006/59709Complex vibration of flexible elastic shells subjected to transversal and sign-changeable local load in the frame of nonlinear classical theory is studied. A transition from partial to ordinary differential equations is carried out using the higher-order Bubnov-Galerkin approach. Numerical analysis is performed applying theoretical background of nonlinear dynamics and qualitative theory of differential equations. Mainly the so-called Sharkovskiy periodicity is studied.Vadim A. Krysko, Jan Awrejcewicz, Natalya E. Saveleva, and Anton V. Krysko© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DENM/2006/79853The object of considerations is a thin linear-elastic cylindrical shell having a periodic structure along one direction tangent to the shell midsurface. The aim of this paper is to propose a new averaged nonasymptotic model of such shells, which makes it possible to investigate free and forced vibrations, parametric vibrations, and dynamical stability of the shells under consideration. As a tool of modeling we will apply the tolerance averaging technique. The resulting equations have constant coefficients in the periodicity direction. Moreover, in contrast with models obtained by the known asymptotic homogenization technique, the proposed one makes it possible to describe the effect of the period length on the overall shell behavior, called a length-scale effect.Barbara Tomczyk© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DENM/2006/20758Dynamic investigations of multimass discrete-continuous systems having variable moment of inertia are performed. The systems are torsionally deformed and consist of an arbitrary number of elastic elements connected by rigid bodies. The problem is nonlinear and it is linearized after appropriate transformations. It is shown that such problems can be investigated using the wave approach. Some analytical considerations and numerical calculations are done for a two-mass system with a special case of boundary conditions.Amalia Pielorz and Monika Skóra© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DENM/2006/75290This paper studies the effect of variable viscosity on the transient Couette flow of dusty fluid with heat transfer between parallel plates. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field is applied perpendicular to the plates. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below. The upper plate is moving with a uniform velocity while the lower is kept stationary. The governing nonlinear partial differential equations are solved numerically and some important effects for the variable viscosity and the uniform magnetic field on the transient flow and heat transfer of both the fluid and dust particles are indicated.Hazem A. Attia© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DENM/2006/90616We establish long-time and large-data existence of a weak solution to the problem describing three-dimensional unsteady flows of an incompressible fluid, where the viscosity and heat-conductivity coefficients vary with the temperature. The approach reposes on considering the equation for the total energy rather than the equation for the temperature. We consider the spatially periodic problem.Eduard Feireisl and Josef Málek© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DENM/2006/71717Solutions for a class of nonlinear second-order differential equations arising in steady Poiseuille flow of an Oldroyd six-constant model are obtained using the quasilinearization technique. Existence, uniqueness, and analyticity results are established using Schauder theory. Numerical results are presented graphically and salient features of the solutions are discussed.F. Talay Akyildiz and K. Vajravelu© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DENM/2006/56146Dynamics of two coupled periodically driven oscillators is analyzed via approximate effective equation of motion. The internal motion is separated off exactly and then approximate equation of motion is derived. Perturbation analysis of the effective equation is used to study the dynamics of the initial dynamical system.Andrzej Okniński and Jan Kyzioł© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DENM/2006/86816This paper deals with the modelling of complex sociopsychological games and reciprocal feelings involving interacting individuals. The modelling is based on suitable developments of the methods of mathematical kinetic theory of active particles with special attention to modelling multiple interactions. A first approach to complexity analysis is proposed referring to both computational and modelling aspects.Nicola Bellomo and Bruno Carbonaro© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DENM/2006/18572In classical particle mechanics, it is well understood that while working with nonholonomic and nonideal constraints, one cannot expect that the constraint be workless. It is curious that in continuum mechanics, however, the implications of the result in classical mechanics have not been clearly understood. In this paper, we show that in dealing with the response of dissipative systems, one cannot require that constraints do no work or ignore the fact that the material response functions depend on the constraint reaction. An example of this is the viscosity of a fluid depending on the pressure.K. R. Rajagopal and Giuseppe Saccomandi© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DENM/2006/68748This paper is devoted to the study of the elasticity with porous dissipation. In the context of the nonlinear problem, we prove instability and nonexistence of solutions. In the context of the linear problem, we obtain exponential growth. We also obtain uniqueness of solutions of the backward in time problem of the linear equations.M. C. Leseduarte and R. Quintanilla© 2009, Hindawi Publishing Corporation. All rights reserved.