Related papers: Numerical solution of a nonlinear eigenvalue probl…
Theory and numerical simulations of the Navier-Stokes equations are used to unravel the inertia-driven dewetting dynamics of an ultrathin film of Newtonian liquid deposited on a solid substrate. A classification of the film thinning regimes…
The objective of this work is to study the role of shear on the rupture of ultrathin polymer films. To do so, a finite-difference numerical scheme for the resolution of the thin film equation was set up taking into account capillary and van…
Numerical modeling of strength and non-destructive testing of complex structures such as buildings, space rockets or oil reservoirs often involves calculations on extremely large grids. The modeling of elastic wave processes in solids…
In this paper, we investigate a class of nonlinear eigenvalue problems resulting from quantum physics. We first prove that the eigenfunction cannot be a polynomial on any open set, which may be reviewed as a refinement of the classic unique…
We construct the asymptotic approximation to the first eigenvalue and corresponding eigensolution of Laplace's operator inside a domain containing a cloud of small rigid inclusions. The separation of the small inclusions is characterised by…
A new model description for the numerical simulation of elastic stents is proposed. Based on the new formulation an inf-sup inequality for the finite element discretization is proved and the proof of the inf-sup inequality for the…
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…
This paper deals with the large-scale behaviour of dynamical optimal transport on $\mathbb{Z}^d$-periodic graphs with general lower semicontinuous and convex energy densities. Our main contribution is a homogenisation result that describes…
A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model here introduced is characterized by an energy with two contributions,…
The classical no-slip boundary condition of the Navier-Stokes equations fails to describe the spreading motion of a droplet on a substrate due to the missing small-scale physics near the contact line. In this thesis, we introduce a novel…
We consider the two-dimensional problem of recovering globally in time the heat distribution on the surface of a layer inside of a heat conducting body from two interior temperature measurements. The problem is ill-posed. The approximation…
Rupture is a nonlinear instability resulting in a finite-time singularity as a fluid layer approaches zero thickness at a point. We study the dynamics of rupture in a generalized mathematical model of thin films of viscous fluids with…
This paper is devoted to studying the inflow problem for an ideal polytropic model with non-viscous gas in one-dimensional half space. We showed the existence of the boundary layer in different areas. By employing the energy method, we also…
Lie symmetry method is applied to find analytic solutions of initial-boundary-value problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a…
The optimal exponentials of the thickness in the geometry rigidity inequality of shells represent the geometry rigidity of the shells. We obtain that the lower bounds of the optimal exponentials are $4/3,$ $3/2,$ and $1,$ for the hyperbolic…
It is shown that for thin metal films, thickness of which does not exceed a thickness of a skin-layer, the problem allows analytical solution for any boundary conditions. The analysis of transmission, reflection and absorption of an…
This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…
We analyze the general problem of determining optimally dense packings, in a Euclidean or hyperbolic space, of congruent copies of some fixed finite set of bodies. We are strongly guided by examples of aperiodic tilings in Euclidean space…
We present a ${\Gamma}$-convergence approximation for the total anisotropic length of a partition. This theoretical result gives rise to a numerical method which allows the study of minimal partitions with respect to different anisotropies.…
We develop an optimization-based approach to the problem of reconstructing temperature-dependent material properties in complex thermo-fluid systems described by the equations for the conservation of mass, momentum and energy. Our goal is…