Related papers: On Existence and Uniqueness of the Solution of a T…
This paper investigates the solutions to the two-phase Serrin's problem, an overdetermined boundary value problem motivated by shape optimization. Specifically, we study the torsional rigidity of composite beams, where two distinct…
In this article, we present various numerical methods to solve multi-contact problems within the Non-Smooth Discrete Element Method. The techniques considered to solve the frictional unilateral conditions are based both on the bi-potential…
The 2-sets convex feasibility problem aims at finding a point in the intersection of two closed convex sets $A$ and $B$ in a normed space $X$. More generally, we can consider the problem of finding (if possible) two points in $A$ and $B$,…
The steady problem resulting from a mixture of two distinct fluids of power-law type is analyzed in this work. Mathematically, the problem results from the superposition of two power laws, one for a constant power-law index with other for a…
We develop a sharp-interface model for solid-state dewetting of double-bubble thin films using an energy variational approach based on a newly proposed interfacial energy. This model characterizes the dynamic evolution of interfaces in…
In this paper we study the viscous simplified Bardina equation on the two-dimensional closed manifold $M$ which is embedded in $\mathbb{R}^3$. First, we prove the existence and the uniqueness of the weak solutions and also the existence of…
We consider a class of singularly perturbed 2-component reaction-diffusion equations which admit bistable traveling front solutions, manifesting as sharp, slow-fast-slow, interfaces between stable homogeneous rest states. In many example…
We consider an abstract mixed variational problem governed by a nonlinear operator $A$ and a bifunctional $J$, in a real reflexive Banach space $X$. The operator $A$ is assumed to be continuous, Lipschitz continuous on each bounded subset…
This paper introduces a modeling framework that is suitable to resolve singularities of impact phenomena encountered in applications. The method involves an exact transformation that turns the continuum, often partial differential equation…
Understanding the contact between solid surfaces is a long standing problem which has a strong impact on the physics of many processes such as adhesion, friction, lubrication and wear. Experimentally, the investigation of solid/solid…
Under the action of a time-periodic external forces we prove the existence of at least one time-periodic weak solution for the interaction between a three-dimensional incompressible fluid, governed by the Navier- Stokes equation and a two…
Based on the global a priori estimates in [Guo-Tice, J. Eur. Math. Soc. (2024)], we establish the well-posedness of a viscous fluid model satisfying the dynamic law for the contact line \begin{equation*}…
In this paper we prove the existence of weak solutions for a thermodynamically consistent phase-field model introduced in [26] in two and three dimensions of space. We use a notion of solution inspired by [18], where the pointwise internal…
We study the time evolution of non-linear viscoelastic solids in the presence of inertia and (self-)contact. For this problem we prove the existence of weak solutions for arbitrary times and initial data, thereby solving an open problem in…
In this paper, we develop a multiscale method for solving the Signorini problem with a heterogeneous field. The Signorini problem is encountered in many applications, such as hydrostatics, thermics, and solid mechanics. It is well-known…
We present a contact mechanics problem, which we consider to be representative for contacts between nominally flat surfaces. The main ingredients of the mathematically fully defined contact problem are: Self-affine roughness, linear…
We study the Plateau problem with a lower dimensional obstacle in $\mathbb{R}^n$. Intuitively, in $\mathbb{R}^3$ this corresponds to a soap film (spanning a given contour) that is pushed from below by a "vertical" 2D half-space (or some…
We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space. The model describes the motion of the film\slash vapor interface…
We investigate the dynamics of finite degree-of-freedom, planar mechanical systems with multiple sliding, unilateral frictional point contacts. A complete classification of systems with 2 sliding contacts is given. The contact-mode based…
Stability of equilibrium states in mechanical systems with multiple unilateral frictional contacts is an important practical requirement, with high relevance for robotic applications. In our previous work, we theoretically analyzed…