Scielo RSS <![CDATA[Computational & Applied Mathematics]]> vol. 28 num. 2 lang. en <![CDATA[SciELO Logo]]> <![CDATA[<b>Periodic solutions for nonlinear telegraph equationvia elliptic regularization</b>]]> In this work we are concerned with the existence and uniqueness of T -periodic weak solutions for an initial-boundary value problem associated with nonlinear telegraph equations typein a domain <img border=0 src="../../../../../../img/revistas/cam/v28n2/a01txt01.gif" align=absmiddle>. Our arguments rely on elliptic regularization technics, tools from classical functional analysis as well as basic results from theory of monotone operators. <![CDATA[<b>On the generalized nonlinear ultra-hyperbolic heatequation related to the spectrum</b>]]> In this paper, we study the nonlinear equation of the form <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02ent02.gif"> where is <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02tex03.gif" align=absmiddle>the ultra-hyperbolic operator iterated k-times, defined by <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02ent03.gif" align=absmiddle>, p + q = n is the dimension of the Euclidean space <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02tex02.gif" align=absmiddle>n, (x, t) = (x1, x2,..., xn, t) <img border=0 src="../../../../../../img/revistas/cam/v28n2/a01ent09.gif" align=absmiddle><img border=0 src="../../../../../../img/revistas/cam/v28n2/a02tex02.gif" align=absmiddle>n× (0, <img border=0 src="../../../../../../img/revistas/cam/v28n2/a06tex01.gif">), k is a positive integer and c is a positive constant. On the suitable conditions for f , u and for the spectrum of the heat kernel, we can find the unique solution in the compact subset of <img border=0 src="../../../../../../img/revistas/cam/v28n2/a02tex02.gif" align=absmiddle>n × (0, <img border=0 src="../../../../../../img/revistas/cam/v28n2/a06tex01.gif">). Moreover, if we put k = 1 and q = 0 we obtain the solution of nonlinear equation related to the heat equation. Mathematical subject classification: 35L30, 46F12, 32W30. <![CDATA[<b>A filter SQP algorithm without a feasibility restoration phase</b>]]> In this paper we present a filter sequential quadratic programming (SQP) algorithm for solving constrained optimization problems. This algorithm is based on the modified quadratic programming (QP) subproblem proposed by Burke and Han, and it can avoid the infeasibility of the QP subproblem at each iteration. Compared with other filter SQP algorithms, our algorithm does not require any restoration phase procedure which may spend a large amount of computation. We underline that global convergence is derived without assuming any constraint qualifications. Preliminary numerical results are reported. <![CDATA[<b>Effect of Hall current on the velocity and temperature distributions of Couette flow with variable properties and uniform suction and injection</b>]]> The unsteady hydromagnetic Couette flow and heat transfer between two parallel porous plates is studied with Hall effect and temperature dependent properties. The fluid is acted upon by an exponential decaying pressure gradient and an external uniform magnetic field. Uniform suction and injection are applied perpendicularly to the parallel plates. Numerical solutions for the governing non-linear equations of motion and the energy equation are obtained. The effect of the Hall term and the temperature dependent viscosity and thermal conductivity on both the velocity and temperature distributions is examined. <![CDATA[<b>The bounded solutions to nonlinear fifth-order differential equations with delay</b>]]> In this paper, we improve some boundedness results, which have been obtained with respect to nonlinear differential equations of fifth order without delay, to a certain functional differential equation with constant delay. We give an illustrative example and also verify our main result by means of Liaponov tecnique. <![CDATA[<b>Lavrentiev-prox-regularization for optimal controlof PDEs with state constraints</b>]]> A Lavrentiev prox-regularization method for optimal control problems with point-wise state constraints is introduced where both the objective function and the constraints are regularized. The convergence of the controls generated by the iterative Lavrentiev prox-regularization algorithm is studied. For a sequence of regularization parameters that converges to zero, strong convergence of the generated control sequence to the optimal control is proved. Due to the proxcharacter of the proposed regularization, the feasibility of the iterates for a given parameter can be improved compared with the non-prox Lavrentiev-Regularization.