Prof. Dumitru Motreanu, University of Perpignan, Department of Mathematics, Perpignan, FRANCE, e-mail: firstname.lastname@example.org
"Qualitative Analysis of Some Quasi-Linear Elliptic Problems"
This work deals with a class of quasi-linear elliptic equations, which are driven by (p,q)-Laplacian operator and fully depend on the solution and the gradient of the solution. The general gradient dependence prevents the use of variational methods. Through the theory of pseudo-monotone operators and the method of subsolutions-supersolutions, we prove existence and regularity results. By using the strong maximum principle we are able to discuss the presence of constant-sign solutions and of nodal (i.e., sign-changing) solutions. In this respect we establish a location principle for nodal solutions showing that, under certain conditions, a nodal solution is enclosed by opposite constant-sign solutions. We also focus on the existence of extremal (or barrier) solutions and their properties.
Prof. Adela Ionescu, Univ of Craiova, Dep. of Applied Mathematics, ROMANIA, e-mail: email@example.com
"Computational and Analytical Results for the Behavior of the Dynamical System Associated to Mixing Flow Model"
The mixing flow theory appears in an area with far from complete solving problems: the flow kinematics. Its methods and techniques developed the significant relation between turbulence and chaos.
In the present paper there are presented recent results concerning the behavior of the mixing flow dynamical system. Both computational and analytical standpoint are taken into account. From computational standpoint, the challenge is great, as the simulation parameters involve strong nonlinearities for the models, both in 2D and 3D case. Therefore this dynamical system can be considered in the category of the so-called
"far from equilibrium systems", widespread between the models of excitable media.
From analytical standpoint, the feedback linearisation of this dynamical system issue special interpretations. This technique contains two fundamental nonlinear controller design techniques: input-output linearization and state-space linearization. The approach is usually referred as input-output linearization or feedback linearization and is based on concepts from nonlinear systems theory. The resulting controller includes the inverse of the dynamic model of the process, providing that such an inverse exists.
The results will be used for further analysis of 3D mixing flow dynamical system.