The kickoff meeting of the project is planned for May 18, 2018 and it will take place at the Faculty of Electrical Engineering and Computing (Unska 3, Zagreb) in the White hall. The meeting will start with presentation of the project to scientific community, followed by several invited talks in the area of diffusion driven systems, which are close to the subjects of the project. If you are interested in participating in the kickoff meeting and workshop, please contact the organizers. 

Confirmed speakers

• Nenad Antonić (University of Zagreb, Faculty of Science, Dept. of Mathematics)
• Mladen Jurak (University of Zagreb, Faculty of Science, Dept. of Mathematics)
• Josipa Pina Milišić (University of Zagreb, Faculty of Electrical Engineering and Computing)
• Boris Muha (University of Zagreb, Faculty of Science, Dept. of Mathematics)
• Nikola Sandrić (University of Zagreb, Faculty of Science, Dept. of Mathematics)

Agenda

Talks

• Nenad Antonić - Parabolic equations as Friedrichs systems
• Abstract: Symmetric positive systems of first-order linear partial differential equations were introduced by Kurt Otto Friedrichs (1958) in order to treat the equations that change their type, like the equations modelling the transonic fluid flow. Friedrichs showed that this class of problems encompasses a wide variety of classical and neoclassical initial and boundary value problems for various linear partial differential equations, such as boundary value problems for some elliptic systems, the Cauchy problem for linear symmetric hyperbolic systems, mixed initial and boundary value problem for hyperbolic equations, and, last but not the least, boundary value problems for equations of mixed type, such as the Tricomi equation. Friedrichs' main goal was to systematically derive the type of conditions that have to be imposed on various parts of the boundary, such as it was done by Cathleen Synge Morawetz in the case of Tricomi's equation. After discussing the state of the art in the abstract theory of Friedrichs systems, we shall discuss some applications to parabolic equations, homogenisation and nonstationary approach to them.                                                                                                                                                                                                                                                                                                                                                    
• Mladen Jurak - Compositional liquid-gas flow in porous media
• Abstract: We study a system of equations governing liquid and gas flow  in porous media. The gas phase is homogeneous while the liquid phase is composed of a liquid component and dissolved gas component. It is assumed that the gas component is weakly soluble in the liquid. The problem is motivated by an application to gas migration in an underground nuclear waste repository. We formulate a weak solution of the initial-boundary value problem and prove the existence theorem by passing to the limit in regularizations of the problem. Hypothesis of low solubility is given precise mathematical meaning.
   
• Josipa Pina Milišić - About cross-diffusion system modeling biofilm growth
• Abstract: In this talk we present our recent result on a well-posedness of a parabolic cross-diffusion model describing multi-species biofilm community. The model of our interest, proposed by Rahman, Sudarsan and Eberl, exhibits a porous medium-type degeneracy when the total biomass vanishes as well as a superdiffusion-type singularity when the biomass reaches its maximum cell capacity, which make the analysis extremely challenging. The system also admits a very interesting non-standard entropy structure which we intensively use in order to show the well-possedeness of the model.  We discuss the existence of global-in-time weak solutions, study the asymptotic behavior and the uniqueness of the solutions, and complement the analysis by numerical simulations that illustrate the theoretically obtained results.                                                                                                                                                                                                              
• Boris Muha - Rigorous derivation of a sixth order thin film equation

• Abstract: In this talk we will study a linear 3D/3D fluid-structure interaction between a thin layer of a viscous fluid and a thin elastic body. First, suitable a priori estimates in terms of thickness of the fluid layer and the elastic body, which are both small parameters, will be derived. Using the obtained estimates we will identify the scaling properties of the physical parameters which give rise to a sixth-order thin film equation, which describes the evolution of the thin elastic body interacting with the thin layer of the fluid. We will analyze the convergence of solutions as small parameter (thickness of the domain) tends to zero and possible extensions to the non-linear case will be discussed. This is joined work with M. Bukal.                                                                                                     

• Nikola Sandrić - Stability of the overdamped Langevin equation in Landau potential 
• Abstract: In this talk, we will discuss stability of the one-dimensional overdamped Langevin equation in Landau potential. We will determine unstable and stable equilibria, and discuss the rate of convergence to stable ones. Also, we will derive conditions for stability of general diffusion processes which generalise the classical and well-known results by R. Khasminskii.

Organizers

• Mario Bukal (University of Zagreb, Faculty of Electrical Engineering and Computing)
• Marko Erceg (University of Zagreb, Faculty of Science, Dept. of Mathematics)
• Anja Vrbaški (University of Zagreb, Faculty of Mining, Geology and Petroleum Engineering)