Related papers: Numerical solution of a nonlinear eigenvalue probl…
Shape optimization problems for interior eigenvalues is a very challenging task since already the computation of interior eigenvalues for a given shape is far from trivial. For example, a concrete maximizer with respect to shapes of fixed…
We discuss the initial boundary value problem for a heat equation in a domain surrounded by a layer. The main features of this problem are twofold: on one hand, the layer is thin compared to the scale of the domain, and on the other hand,…
We analyze an optimization problem of the conductivity in a composite material arising in a heat conduction energy storage problem. The model is described by the heat equation that specifies the heat exchange between two types of materials…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
A shape optimization problem arising from the optimal reinforcement of a membrane by means of one-dimensional stiffeners or from the fastest cooling of a two-dimensional object by means of ``conducting wires'' is considered. The criterion…
We study a shape optimization problem involving a solid $K\subset\mathbb{R}^n$ that is maintained at constant temperature and is enveloped by a layer of insulating material $\Omega$ which obeys a generalized boundary heat transfer law. We…
We study a free boundary problem arising from the theory of thermal insulation. The outstanding feature of this set optimization problem is that the boundary of the set being optimized is not a level surface of a harmonic function, but…
Motion in the atmosphere or mantle convection are two among phenomena of natural convection induced by internal heat sources. They bifurcate from the conduction state as a result of its loss of stability. In spite of their importance, due…
This work presents a mathematical model for the optimal control of thin-film flows over a flexible topography influenced by an external force. Our thin-film model allows for the rupture of films as well as the coalescence of bubbles. The…
We report on the numerical implementation of thin film equations that describe the capillary-driven evolution of viscous films, in two-dimensional configurations. After recalling the general forms and features of these equations, we focus…
We consider the problem of camouflaging for bodies with specular surface in the framework of geometric optics. The index of visibility introduced in [Plakhov 2017] measures the mean deviation of light rays incident on the body's surface. We…
In this manuscript, we solve a nonlinear optimization problem in the study of maximizing cooling temperature using inhomogeneous thermoelectric materials.
The large time behavior of non-negative weak solutions to a thin film approximation of the two-phase Muskat problem is studied. A classification of self-similar solutions is first provided: there is always a unique even self-similar…
In this Letter we investigate the rupture instability of thin liquid films by means of a bifurcation analysis in the vicinity of the short-scale instability threshold. The rupture time estimate obtained in closed form as a function of the…
In this paper we consider a minimization problem of the type $$ I_{\beta,p}(D;\Omega)=\inf\biggl\{\int_\Omega \lvert{D\phi}\rvert^pdx+\beta \int_{\partial^* \Omega}\lvert{\phi}\rvert^pd\mathcal{H}^{n-1},\; \phi \in W^{1,p}(\Omega),\;\phi…
This article is devoted to the study of spectral optimisation for inhomogeneous plates. In particular, we optimise the first eigenvalue of a vibrating plate with respect to its thickness and/or density. Our result is threefold. First, we…
We consider the transmission eigenvalue problem for an impenetrable obstacle with Dirichlet boundary condition surrounded by a thin layer of non-absorbing inhomogeneous material. We derive a rigorous asymptotic expansion for the first…
We show the existence and optimal regularity of the optimal temperature configuration in a problem in heat conduction with minimal temperature constraint, interior heating and exterior insulation. Regularity of the two free boundaries is…
Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…
This paper investigates shape optimization problems in the context of heat transfer, with a focus on the stability and non-optimality of round domains under Robin boundary conditions. Using the flow approach and Steklov eigenvalue…