On a system of nonlinear PDE's for phase transitions with vector order parameter and convective effect

AbstractThe paper deals with a system of nonlinear PDE's which describes a phase-field model with convection and temperature dependent constraint to the vector order parameter. Existence of solutions for the system under consideration is proved by the method of Yosida approximation and fixed point arguments

Oscillations of vector differential equations of hyperbolic type with functional arguments

Vector hyperbolic differential equations with functional arguments are studied, and oscillations of solutions of certain boundary value problems are investigated. The approach used is to reduce the multi-dimensional oscillation problems to the nonexistence of positive solutions of scalar functional differential inequalities by employing the concept of H-oscillation introduced by Domšlak, where H denotes some unit vector

Estimates of solutions of impulsive parabolic equations and applications to the population dynamics

A theorem on estimates of solutions of impulsive parabolic equations by means of solutions of impulsive ordinary differential equations is proved. An application to the population dynamics is given

Southeastern Europe at the beginning of the 21st century: New dangers, new strategies, new perspectives. ZEI Discussion Papers: 2001, C 82

Introduction. The war in Kosovo marked the end of a turbulent century for the whole of South Eastern Europe. A century of perils, bloodsheds and suffering. The beginning of the new century was connected with the hope for peace at last, for a stable and prosperous region able to be integrated into the United Europe. But this kind of a peace has not come yet. The real peace, expected and even dreamed for in the region should be a new peace order, that will make future wars on the Balkans impossible, a peace order that will bring at last stability and prosperity in this impoverished and turbulent part of Europe. Such a peace is not achieved yet with the stationing of the KFOR and the establishing of the UNMIK administration in Kosovo, is even endangered with the new outbursts of fighting in South Serbia and Macedonia, but nevertheless for the first time in the long and tragic Balkan history is closer than ever. The dawn of a new future for the Balkans opening a bright perspective for all Balkan post-communist societies is glimmering already over the horizon. The intent of the international community, of the NATO and the EU to introduce the Stability Pact for South Eastern Europe with its ultimate goal - the integration of the region into the EU structures are a strong guarantee, that this future will come into existence. However, this future is still a distant one. There is a long way until it could be reached and the politicians together with the experts should warn from overoptimistic expectations. Very often such expectations give way to bitter disappointments and such developments should be avoided in the region. Because the legacy and the forces of the past, the inertia of the past are still very strong. Because the tasks for stabilising and transforming the Balkans are without a parallel in the region’s history. The challenge is of such a proportion that the international community and Balkan societies should be prepared for long and difficult efforts and uneasy victories until the goal appears within reach. Winning in Kosovo was just winning the first battle in the long war for the European future of the Balkans. Stopping after the first win and not trying to develop it further we start to face the danger of restoring the pre-war situation dominated by ethnic hatred and ethnic cleansing, but with a role swap - the victims and the oppressors just change places. If the international community allows this to happen and to prevail, then all the efforts and all the suffering would be in vain. To go further means that we should try to break the vicious circle of ethnic animosity, means much more efforts, much more economic and financial burdens and may-be less spectacular victories. The already starting to appear "Balkan fatigue" may divert the attention of the world public opinion or make some projects politically unpopular. Some regional setbacks could have a negative impact on the Western readiness to pursue this costly strategy. One of the ways to counter this "Balkan fatigue" is to explore the possibility for such setbacks, to identify the probable traps and to suggest alternative solutions for the most acute regional problems, if a traditional approach could not bring the expected results

Estimates of solutions of impulsive parabolic equations and applications to the population dynamics

A theorem on estimates of solutions of impulsive parabolic equations by means of solutions of impulsive ordinary differential equations is proved. An application to the population dynamics is given

On the stability of solutions of impulsive nonlinear parabolic equations

Stability and asymptotic stability of the solutions of impulsive nonlinear pa ra bo lic equations are studied via the method of differential inequalities