Related papers: Existence and uniqueness results for a nonlinear s…

This paper investigates the stabilization of a coupled system comprising a parabolic PDE and an elliptic PDE with nonlinear terms. A rigorous backstepping design provides an explicit boundary control law and exponentially convergent…

In this paper we investigate the existence of solutions and their weak-strong uniqueness property for a PDE system modelling damage in viscoelastic materials. In fact, we address two solution concepts, weak and strong solutions. For the…

We prove existence and regularity results for weak solutions of non linear elliptic systems with non variational structure satisfying $(p,q)$-growth conditions. In particular we are able to prove higher differentiability results under a…

In this note we extend to the random, stationary ergodic setting previous results of periodic homogenization for a particular family of nonlinear nonlocal "elliptic" equations with oscillatory coefficients. Such equations include, but are…

In this paper, we discuss the existence and uniqueness of coexistence states for a class of non-local elliptic system. This problem models the behaviour of a bacteria and a living nutrient, whose diffusion depends on the population of the…

This paper examines a system of partial differential equations describing dislocation dynamics in a crystalline solid. In particular we consider dynamics linearized about a state of zero stress and use linear semigroup theory to establish…

We investigate the stabilization of a locally coupled wave equations with only one internal viscoelastic damping of Kelvin-Voigt type. The main novelty in this paper is that both the damping and the coupling coefficients are non smooth.…

A classical 3-D thermoviscoelastic system of Kelvin-Voigt type is considered. The existence and uniqueness of a global regular solution is proved without small data assumption. The existence proof is based on the successive approximation…

In this paper, we establish the existence and uniqueness of solutions of elliptic-parabolic stochastic Keller-Segel systems. The solution is obtained through a carefully designed localization procedure together with some a priori estimates.…

In this paper, we study a nonlocal evolution system. We apply abstract results from the bifurcation theory to obtain the existence of coexistence states. Their stability are investigated as well.

Solutions to the Einstein equation that represent the superposition of static isolated bodies with axially symmetry are presented. The equations nonlinearity yields singular structures (strut and membranes) to equilibrate the bodies. The…

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…

The existence and uniqueness of weak solutions is shown for a system related to the Willis model of elastodynamics. Both the whole space case and the case of a bounded smooth domain are studied. To this end the equations are reformulated as…

We consider the inverse problem of determining some class of nonlinear terms appearing in an elliptic equation from boundary measurements. More precisely, we study the stability issue for this class of inverse problems. Under suitable…

We introduce a system of equations that models a non-isothermal magnetoviscoelastic fluid. We show that the model is thermodynamically consistent, and that the critical points of the entropy functional with prescribed energy correspond…

In this paper we analyze the existence of large positive radial solutions to some quasilinear elliptic systems. Also, a non-radially symmetric solution is obtained by using a lower and upper solution method. The equations are coupled by…

Some systems of parabolic equations with nonlocal initial conditions are studied. The systems arise when considering steady-state solutions to diffusive age-structured cooperative or competing species. Local and global bifurcation…

We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…

We analyze the pattern forming ability and pattern stability for a one-dimensional non-linear transport-diffusion equation on the circle. We show that the trivial steady state is stable when diffusion is sufficiently strong. In the limit…

The qualitative analysis of the initial value problem P related to a non linear third order parabolic equation typical of diffusive models is discussed. Some basic properties of the the fundamental solution of a related linear operator are…