Conveners
Partial Differential Equations and Applications
- Josip Tambača
Partial Differential Equations and Applications
- Marko Erceg (University of Zagreb, Croatia)
Partial Differential Equations and Applications
- Andrijana Ćuković
We present a novel numerical method for optimal design problems in the setting of the Kirchhoff-Love model, where the mechanical behaviour of the domain is modeled with fourth order elliptic
equation, and we restrict ourselves to domains filled with two isotropic elastic materials.
Since the classical solution usually does not exist, we use homogenization theory to prove general existence...
In this talk, we propose mathematical tools for studying oscillation and concentration effects at infinity in sequences of absolutely continuous functions. These tools can be applied beyond the classical setting, especially in cases where the fundamental theorem of Young measures or the fundamental theorem of H-measures cannot be used. Examples of aforementioned cases have already been studied...
In this work we consider a planar periodic network of elastic rods. As the model for a structure made of elastic rods we use a one-dimensional model of Naghdi/Timošenko type allowing for membrane, stretching and bending deformations with the Kirchhoff type junction conditions. Using a mesh two-scale convergence, a variant of the two-scale convergence adapted for models given on...
We consider long-time behavior of solutions to the thin-film equation $ \partial_th = -\partial_x(h \partial_x^3h)$ on the real line with initial datum of finite second moment. The equation describes the interface dynamics of a thin fluid neck of thickness $2h(x,t)$ in the Hele-Shaw cell. Upon rescaling the equation in such a way that the second moment is constant in time, precise rate of...
In this talk, the starting point of our analysis is coupled system of elasticity and weakly compressible fluid. We consider two small parameters: the thickness $h$ of the thin plate and the pore scale $\varepsilon_h$ which depend on $h$. We will focus specifically on the case when the pore size is small relative to the thickness of the plate. The main goal here is derive a model for a...
Solving parameter-dependent Partial Differential Equations (PDE) for multiple parameters is often needed in physical, biomedical and engineering applications.Usually,PDEs are solved by transforming PDE to weak formulation. Usually, approximation of the solutions is found in finite-dimensional function space using Finite Element Method. This results in large number of equations and solving them...
In this talk, we present regularity results for entropy solutions to a family of second order degenerate (the diffusion matrix is only positive semi-definite) parabolic partial differential equations under a quantitative variant of the non-degeneracy condition. The proof is based on the kinetic reformulation, which allows for estimating the solution on the Littlewood-Paley dyadic blocks of the...
The theory of abstract Friedrichs operators, introduced by
Ern, Guermond and Caplain (2007), proved to be a successful setting
for studying positive symmetric systems of first order partial
differential equations (Friedrichs, 1958),
nowadays better known as Friedrichs systems.
Recently, a characterisation of abstract Friedrichs operators in terms of skew-symmetric operators and bounded...
We study the motion of a rigid body within a compressible, isentropic, and viscous fluid contained in a fixed bounded domain $\Omega \subset \mathbb{R}^3$. The fluid's behavior is described by the Navier-Stokes equations, while the motion of the rigid body is governed by ordinary differential equations representing the conservation of linear and angular momentum. We prescribe a...
The fluid temperature in a heat conduction problem in a dilated pipe with a small circular cross-section is considered. The fluid flow is governed by the pressure drop. The heat exchange between the fluid and the environment is described by Newton’s cooling law and the temperature is described by the convection-diffusion equation with a stationary Poiseuille velocity. Due to pipe dilation, the...
We consider a system of nonlinear partial differential equations that describes two-phase, two-component fluid flow in porous media. The system equations are obtained from the mass conservation law written for each component, to which initial and boundary conditions are added. For main unknows we select persistent variables, capable of modelling the flow in both the two-phase flow and the...
We study the system of partial differential equations describing a two-phase two-component flow in heterogeneous porous media. The unknowns of the problem are global pressure, gas pseudo-pressure and capillary pseudo-pressure, artificial persistent variables that describe the flow both in the two-phase and single-phase regions and at the same time allow to decouple the starting equations....
