http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2012, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijde/2012/587208/Numerical solution of the modified equal width wave equation is obtained by using lumped Galerkin method based on cubic B-spline finite element method. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. Accuracy of the proposed method is discussed by computing the numerical conserved laws L2 and L∞ error norms. The numerical results are found in good agreement with exact solution. A linear stability analysis of the scheme is also investigated.Seydi Battal Gazi Karakoç and Turabi GeyikliCopyright © 2012 Seydi Battal Gazi Karakoç and Turabi Geyikli. All rights reserved.http://www.hindawi.com/journals/ijde/2011/319375/We study a system of infinitely many Riccati equations that arise from a cumulant control problem, which is a generalization of regulator problems, risk-sensitive controls, minimal cost variance controls, and k-cumulant controls. We obtain estimates for the existence intervals of solutions of the system. In particular, new existence conditions are derived for solutions on the horizon of the cumulant control problem.Stanley R. Liberty and Libin MouCopyright © 2011 Stanley R. Liberty and Libin Mou. All rights reserved.http://www.hindawi.com/journals/ijde/2011/520840/Advection equations appear often in large-scale mathematical models arising in many fields of science and engineering. The Crank-Nicolson scheme can successfully be used in the numerical treatment of such equations. The accuracy of the numerical solution can sometimes be increased substantially by applying the Richardson Extrapolation. Two theorems related to the accuracy of the calculations will be formulated and proved in this paper. The usefulness of the combination consisting of the Crank-Nicolson scheme and the Richardson Extrapolation will be illustrated by numerical examples.Zahari Zlatev, Ivan Dimov, István Faragó, Krassimir Georgiev, Ágnes Havasi, and Tzvetan OstromskyCopyright © 2011 Zahari Zlatev et al. All rights reserved.http://www.hindawi.com/journals/ijde/2011/628459/We study stochastic partly dissipative lattice systems with random coupled coefficients and multiplicative/additive white noise in a weighted space of infinite sequences. We first show that these stochastic partly dissipative lattice differential equations generate a random dynamical system. We then establish the existence of a tempered random bounded absorbing set and a global compact random attractor for the associated random dynamical system.Xiaoying HanCopyright © 2011 Xiaoying Han. All rights reserved.http://www.hindawi.com/journals/ijde/2011/356356/We are interested in the existence of solutions for Dirichlet problem associated to the degenerate quasilinear elliptic equations -∑j=1nDj[ω2(x)Aj(x,u,∇u)]+ω1(x)g(x,u(x))+H(x,u,∇u)  ω2(x)=f(x),  on  Ω in the setting of the weighted Sobolev spaces W01,p(Ω,ω1,ω2).Albo Carlos CavalheiroCopyright © 2011 Albo Carlos Cavalheiro. All rights reserved.http://www.hindawi.com/journals/ijde/2011/679528/A high-order iterative scheme is established in order to get a convergent sequence at a rate of order N (N≥1) to a local unique weak solution of a nonlinear Kirchhoff wave equation in the unit membrane. This extends a recent result in (EJDE, 2005, No. 138) where a recurrent sequence converges at a rate of order 2.Le Thi Phuong Ngoc and Nguyen Thanh LongCopyright © 2011 Le Thi Phuong Ngoc and Nguyen Thanh Long. All rights reserved.http://www.hindawi.com/journals/ijde/2011/751969/We consider the dead-core problem for the fast diffusion equation with spatially dependent coefficient and obtain precise estimates on the single-point final dead-core profile. The proofs rely on maximum principle and require much delicate computation.Zhengce Zhang and Biao WangCopyright © 2011 Zhengce Zhang and Biao Wang. All rights reserved.http://www.hindawi.com/journals/ijde/2011/801706/We prove the existence of weak solution to a semilinear boundary value problem without the Landesman-Lazer condition.Sikiru Adigun SanniCopyright © 2011 Sikiru Adigun Sanni. All rights reserved.http://www.hindawi.com/journals/ijde/2011/408704/We investigate a fractional diffusion/anti-diffusion equation proposed by Andrew C. Fowler to describe the dynamics of sand dunes sheared by a fluid flow. In this paper, we prove the global-in-time well-posedness in the neighbourhood of travelling-waves solutions of the Fowler equation.Afaf BouharguaneCopyright © 2011 Afaf Bouharguane. All rights reserved.http://www.hindawi.com/journals/ijde/2011/404276/This paper contains a surprisingly large amount of material and indeed can serve as an introduction to some of ideas and methods of singular perturbation theory. The work done in this area during the periods 1984–2000 and 2000–2005 has already been surveyed in 2002 and 2007 but our main objective is to produce a collection of important research articles of physical significance. In this paper, the crux of research articles published by numerous researchers during 2006–2010 in referred journals has been presented, and this leads to conclusions and recommendations about what methods to use on singular perturbation problems.Manoj Kumar and ParulCopyright © 2011 Manoj Kumar and Parul. All rights reserved.http://www.hindawi.com/journals/ijde/2011/913125/We consider in this paper an abstract parabolic backward Cauchy problem associated with an unbounded linear operator in a Hilbert space H, where the coefficient operator in the equation is an unbounded self-adjoint positive operator which has a continuous spectrum and the data is given at the final time t=T and a solution for 0≤t<T is sought. It is well known that this problem is illposed in the sense that the solution (if it exists) does not depend continuously on the given data. The method of regularization used here consists of perturbing both the equation and the final condition to obtain an approximate nonlocal problem depending on two small parameters. We give some estimates for the solution of the regularized problem, and we also show that the modified problem is stable and its solution is an approximation of the exact solution of the original problem. Finally, some other convergence results including some explicit convergence rates are also provided.Salah Djezzar and Nihed TeniouCopyright © 2011 Salah Djezzar and Nihed Teniou. All rights reserved.http://www.hindawi.com/journals/ijde/2011/989065/A new iterative method introduced by Daftardar-Gejji and Jafari (2006) (DJ Method) is an efficient technique to solve nonlinear functional equations. In the present paper, sufficiency conditions for convergence of DJM have been presented. Further equivalence of DJM and Adomian decomposition method is established.Sachin Bhalekar and Varsha Daftardar-GejjiCopyright © 2011 Sachin Bhalekar and Varsha Daftardar-Gejji. All rights reserved.http://www.hindawi.com/journals/ijde/2011/619623/In this paper, we construct and verify the asymptotic expansion for the spectrum of a boundary-value problem in a unit circle periodically perforated along the boundary. It is assumed that the size of perforation and the distance to the boundary of the circle are of the same smallness. As an application of the obtained results, the asymptotic behavior of the best constant in a Friedrichs-type inequality is investigated.G. A. Chechkin, Yu. O. Koroleva, L.-E. Persson, and P. WallCopyright © 2011 G. A. Chechkin et al. All rights reserved.http://www.hindawi.com/journals/ijde/2011/453727/We deal with fully nonlinear second-order equations assuming a superlinear growth in u with the aim to generalize previous existence and uniqueness results of viscosity solutions in the whole space without conditions at infinity. We also consider the solvability of the Dirichlet problem in bounded and unbounded domains and show a blow-up result.G. Galise and A. VitoloCopyright © 2011 G. Galise and A. Vitolo. All rights reserved.http://www.hindawi.com/journals/ijde/2011/261963/We present a constructive approach to establish existence and uniqueness of solution of singular boundary value problem -(p(x)y′(x))′=q(x)f(x,y,py′) for 0<x≤b,y(0)=a,α1y(b)+β1p(b)y′(b)=γ1. Here p(x)>0 on (0,b) allowing p(0)=0. Further q(x) may be allowed to have integrable discontinuity at x=0, so the problem may be doubly singular.R. K. Pandey and Amit K. VermaCopyright © 2011 R. K. Pandey and Amit K. Verma. All rights reserved.http://www.hindawi.com/journals/ijde/2011/259805/A class of nonautonomous two-species competitive system with stage structure and impulse is considered. By using the continuation theorem of coincidence degree theory, we derive a set of easily verifiable sufficient conditions that guarantee the existence of at least a positive periodic solution, and, by constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are presented. Finally, an illustrative example is given to demonstrate the correctness of the obtained results.Changjin Xu and Daxue ChenCopyright © 2011 Changjin Xu and Daxue Chen. All rights reserved.http://www.hindawi.com/journals/ijde/2011/198606/Carlson's type theorem on removable sets for α-Holder continuous solutions is investigated for the quasilinear elliptic equations div A(x,u,∇u)=0, having degeneration ω in the Muckenhoupt class. In partial, when α is sufficiently small and the operator is weighted p-Laplacian, we show that the compact set E is removable if and only if the Hausdorff measure Λω−p+(p−1)α(E)=0.Farman I. Mamedov, Aslan D. Quliyev, and Mirfaig M. MirheydarliCopyright © 2011 Farman I. Mamedov et al. All rights reserved.http://www.hindawi.com/journals/ijde/2011/978387/A SI-type ecoepidemiological model that incorporates reproduction delay of predator is studied. Considering delay as parameter, we investigate the effect of delay on the stability of the coexisting equilibrium. It is observed that there is stability switches, and Hopf bifurcation occurs when the delay crosses some critical value. By applying the normal form theory and the center manifold theorem, the explicit formulae which determine the stability and direction of the bifurcating periodic solutions are determined. Computer simulations have been carried out to illustrate different analytical findings. Results indicate that the Hopf bifurcation is supercritical and the bifurcating periodic solution is stable for the considered parameter values. It is also observed that the quantitative level of abundance of system populations depends crucially on the delay parameter if the reproduction period of predator exceeds the critical value.N. BairagiCopyright © 2011 N. Bairagi. All rights reserved.http://www.hindawi.com/journals/ijde/2011/896427/We improve some results of Pan and Xing (2008) and extend the exponent range in Liouville-type theorems for some parabolic systems of inequalities with the time variable on R. As an immediate application of the parabolic Liouville-type theorems, the range of the exponent in blow-up rates for the corresponding systems is also improved.Guocai Cai, Hongjing Pan, and Ruixiang XingCopyright © 2011 Guocai Cai et al. All rights reserved.http://www.hindawi.com/journals/ijde/2011/329014/We study the Navier-Stokes-Nernst-Planck-Poisson system modeling the flow of electrohydrodynamics. For small initial data, the global existence, uniqueness, and asymptotic stability as time goes to infinity of self-similar solutions to the Cauchy problem of this system posed in the whole three dimensional space are proved in the function spaces of pseudomeasure type.Jihong Zhao, Chao Deng, and Shangbin CuiCopyright © 2011 Jihong Zhao et al. All rights reserved.http://www.hindawi.com/journals/ijde/2011/535736/The stationary Boussinesq equations describing the heat transfer in the viscous heat-conducting fluid under inhomogeneous Dirichlet boundary conditions for velocity and mixed boundary conditions for temperature are considered. The optimal control problems for these equations with tracking-type functionals are formulated. A local stability of the concrete control problem solutions with respect to some disturbances of both cost functionals and state equation is proved.Gennady Alekseev and Dmitry TereshkoCopyright © 2011 Gennady Alekseev and Dmitry Tereshko. All rights reserved.http://www.hindawi.com/journals/ijde/2011/582512/We employ the bifurcation method of planar dynamical systems and qualitative theory of polynomial differential systems to derive new bounded traveling-wave solutions for a variant of the K(3,2) equation. For the focusing branch, we obtain hump-shaped and valley-shaped solitary-wave solutions and some periodic solutions. For the defocusing branch, the nonexistence of solitary traveling wave solutions is shown. Meanwhile, some periodic solutions are also obtained. The results presented in this paper supplement the previous results.Jiangbo Zhou and Lixin TianCopyright © 2011 Jiangbo Zhou and Lixin Tian. All rights reserved.http://www.hindawi.com/journals/ijde/2011/346298/A fractional order time-independent form of the wave equation or diffusion equation in two dimensions is obtained from the standard time-independent form of the wave equation or diffusion equation in two-dimensions by replacing the integer order partial derivatives by fractional Riesz-Feller derivative and Caputo derivative of order α,β,1<ℜ(α)≤2 and 1<ℜ(β)≤2 respectively. In this paper, we derive an analytic solution for the fractional time-independent form of the wave equation or diffusion equation in two dimensions in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases, the solutions are represented also in terms of Fox's H-function.Anitha ThomasCopyright © 2011 Anitha Thomas. All rights reserved.http://www.hindawi.com/journals/ijde/2011/383294/We consider a kind of Sturm-Liouville boundary value problems. Using variational techniques combined with the methods of upper-lower solutions, the existence of at least one positive solution is established. Moreover, the upper solution and the lower solution are presented.Li Zhang, Xiankai Huang, and Weigao GeCopyright © 2011 Li Zhang et al. All rights reserved.http://www.hindawi.com/journals/ijde/2011/463416/This paper is concerned with time-periodic solution of the weakly dissipative Camassa-Holm equation with a periodic boundary condition. The existence and uniqueness of a time periodic solution is presented.Chunyu ShenCopyright © 2011 Chunyu Shen. All rights reserved.http://www.hindawi.com/journals/ijde/2011/354016/This paper is concerned with a time-varying fishing model with delay. By means of the continuation theorem of coincidence degree theory, we prove that it has at least one positive almost periodic solution.Xia Li, Yongkun Li, and Chunyan HeCopyright © 2011 Xia Li et al. All rights reserved.http://www.hindawi.com/journals/ijde/2011/793023/This paper is concerned with the existence and uniqueness of a mild solution of a semilinear fractional-order functional evolution differential equation with the infinite delay and impulsive effects. The existence and uniqueness of a mild solution is established using a solution operator and the classical fixed-point theorems.Jaydev Dabas, Archana Chauhan, and Mukesh KumarCopyright © 2011 Jaydev Dabas et al. All rights reserved.http://www.hindawi.com/journals/ijde/2011/703189/The object of investigations is a system of impulsive differential equations with “supremum.” These equations are not widely studied yet, and at the same time they are adequate mathematical model of many real world processes in which the present state depends significantly on its maximal value on a past time interval. Practical stability for a nonlinear system of impulsive differential equations with “supremum” is defined and studied. It is applied Razumikhin method with piecewise continuous scalar Lyapunov functions and comparison results for scalar impulsive differential equations. To unify a variety of stability concepts and to offer a general framework for the investigation of the stability theory, the notion of stability in terms of two measures has been applied to both the given system and the comparison scalar equation. An example illustrates the usefulness of the obtained sufficient conditions.S. G. Hristova and A. GeorgievaCopyright © 2011 S. G. Hristova and A. Georgiev. All rights reserved.http://www.hindawi.com/journals/ijde/2011/572824/We obtain some W2,2 a priori bounds for a class of uniformly elliptic second-order differential operators, both in a no-weighted and in a weighted case. We deduce a uniqueness and existence theorem for the related Dirichlet problem in some weighted Sobolev spaces on unbounded domains.Sara Monsurrò, Maria Salvato, and Maria TransiricoCopyright © 2011 Sara Monsurrò et al. All rights reserved.http://www.hindawi.com/journals/ijde/2011/548982/We use generalized differential transform method (GDTM) to derive the solution of space-time fractional telegraph equation in closed form. The space and time fractional derivatives are considered in Caputo sense and the solution is obtained in terms of Mittag-Leffler functions.Mridula Garg, Pratibha Manohar, and Shyam L. KallaCopyright © 2011 Mridula Garg et al. All rights reserved.