Necessary Optimality Conditions for a Dead Oil Isotherm Optimal Control Problem

We study a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of the mechanics of a continuous medium. Recent results on the problem provide existence, uniqueness and regularity of the optimal solution. Here we obtain the first necessary optimality conditions.Comment: 9 page

Generalizations of Gronwall-Bihari Inequalities on Time Scales

We establish some nonlinear integral inequalities for functions defined on a time scale. The results extend some previous Gronwall and Bihari type inequalities on time scales. Some examples of time scales for which our results can be applied are provided. An application to the qualitative analysis of a nonlinear dynamic equation is discussed.Comment: This is a preprint of an article accepted (16/May/2008) for publication in the "Journal of Difference Equations and Applications"; J. Difference Equ. Appl. is available online at http://www.informaworld.co

Combined dynamic Grüss inequalities on time scales

We prove a more general version of the Grüss inequality by using the recent theory of combined dynamic derivatives on time scales and the more general notions of diamond-α derivative and integral. For the particular case where α = 1, one obtains the delta-integral Grüss inequality on time scales in (see M. Bohner and T. Matthews [5]); for α = 0 a nabla-integral Grüss inequality is derived. If we further restrict ourselves by fixing the time scale to the real (or integer) numbers, then the standard continuous (discrete) inequalities are obtained. © 2009 Springer Science+Business Media, Inc

Preface of Special Issue on Optimization and Differential Equations

The present volume is a Special Issue on Optimization and Differential Equations