Related papers: Time-dependent Inclusions and Sweeping Processes i…

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…

The paper addresses the study of a class of evolutionary quasi-variational inequalities of the parabolic type arising in the formation and growth models of granular and cohensionless materials. Such models and their mathematical…

We consider an inverse boundary value problem for the heat equation with a nonsmooth coefficient of conductivity which models the displacement of a moving body inside a nonhomogeneous background. We prove the uniqueness of the moving…

This paper is devoted to studying a system of coupled nonlinear first order history-dependent evolution inclusions in the framework of evolution triples of spaces. The multivalued terms are of the Clarke subgradient or of the convex…

Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…

We consider quasi-static poroelastic systems with incompressible constituents. The nonlinear permeability is taken to be dependent on solid dilation, and physical types of boundary conditions (Dirichlet, Neumann, and mixed) for the fluid…

In this paper, we consider evolution problems involving time dependent maximal monotone operators in Hilbert spaces. Existence and relaxation theorems are proved.

We consider the Sommerfeld problem of diffraction by an opaque half-plane with a real wavenumber interpreting it as the limiting case, as time tends to infinity, of the corresponding time-dependent diffraction problem. We prove that the…

We present our recent study on rough adhesive contacts of viscoelastic materials in steady-state sliding, focusing on the interplay between adhesion and viscoelasticity by means of a novel energy approach. We investigate tribological…

This paper is devoted to a study of time-dependent hemivariational inequality. We prove existence and uniqueness of its solution, provide fully discrete scheme and reformulate this scheme as a series of nonsmooth optimization problems. This…

We consider the planar three-body problem perturbed by a celestial body modeled as a time-dependent perturbation that decays in time. We assume that the motion of the celestial body is given and is unbounded with a non-zero asymptotic…

We prove a global existence result for weak solutions to a one-dimensional free boundary problem with flux boundary conditions describing swelling along a halfline. Additionally, we show that solutions are not only unique but also depend…

We solve the reachability problem for a coupled wave-wave system with an integro-differential term. The control functions act on one side of the boundary. The estimates on the time is given in terms of the parameters of the problem and they…

In this paper, we are concerned with a time-dependent transmission problem for a thermo-piezoelectric elastic body immersed in a compressible fluid. It is shown that the problem can be treated by the boundary-field equation method, provided…

In this paper, we apply the geometric Hamilton--Jacobi theory to obtain solutions of classical hamiltonian systems that are either compatible with a cosymplectic or a contact structure. As it is well known, the first structure plays a…

This paper consists of two parts. In the first part we prove the unique solvability for the abstract variational-hemivariational inequality with history-dependent operator. The proof is based on the existing result for the static…

In any number of space variables, we study the Cauchy problem related to the thin-film equation in the simplest case of a linearly degenerate mobility. This equation, derived from a lubrication approximation, also models the surface tension…

We continue the analysis on the model equation arising in the theory of viscoelasticity $$ \partial_{tt} u(t)-\big[1+k_t(0)\big]\Delta u(t) -\int_0^\infty k'_t(s)\Delta u(t-s) d s + f(u(t)) = g $$ in the presence of a (convex, nonnegative…

Let $C(t)$, $t\geq0$ be a Lipschitz set-valued map with closed and (mildly non-)convex values and $f(t, x,u)$ be a map, Lipschitz continuous w.r.t. $x$. We consider the problem of reaching a target $S$ within the graph of $C$ subject to the…

We prove that on any closed Riemannian three-manifold $(M,g)$ the time-dependent Euler equations are non-mixing on the space of smooth volume-preserving vector fields endowed with the $C^1$-topology, for any fixed helicity and large enough…