Giovanna Bonfanti

Thermal effects in adhesive contact: modelling and analysis

In this paper, we consider a contact problem with adhesion between a viscoelastic body and a rigid support, taking thermal effects into account. The PDE system we deal with is derived within the modelling approach proposed by Fremond and, in particular, includes the entropy balance equations, describing the evolution of the temperatures of the body and of the adhesive material. Our main result shows the existence of global in time solutions (to a suitable variational formulation) of the related initial and boundary value problem.

Existence and uniqueness results to a phase transition model based on microscopic accelerations and movements

Abstract Microscopic movements are responsible for the phase transition at the macroscopic level. The power of the microscopic accelerations of these motions is not neglected, as opposed to some previous works, in the derivation of phase transition models accounting for strong dissipation or irreversible phenomena. Such models lead to nonlinear parabolic–hyperbolic systems. Some existence and uniqueness results are established, through fixed point and regularization arguments, for related Cauchy–Neumann problems.

Regularity and convergence results for a phase–field model with memory

A phase field model based on the Coleman-Gurtin heat flux law is considered. The resulting system of non-linear parabolic equations, associated with a set of initial and Neumann boundary conditions, is studied. Existence, uniqueness, and regularity results are proved. An asymptotic analysis is also carried out, in the case where the coefficient of the interfacial energy term tends to 0.

On the Energy Decay for a Thermoelastic Contact Problem Involving Heat Transfer

A dynamic unilateral contact problem between two thermoelastic beams is considered. Under thermal boundary conditions involving heat transfer, the evolution problem is shown to possess an energy decaying exponentially to zero, as time goes to infinity.

Asymptotic analysis for vanishing acceleration in a thermoviscoelastic system

We have investigated a dynamic thermoviscoelastic system (2003), establishing existence and uniqueness results for a related initial and boundary values problem. The aim of the present paper is to study the asymptotic behavior of the solution to the above problem as the power of the acceleration forces goes to zero. In particular, well-posedness and regularity results for the limit (quasistatic) problem are recovered.

On some abstract variable domain hyperbolic differential equations

The Cauchy problem is studied for a class of linear abstract differential equations of hyperbolic type with variable domain. Existence and uniqueness results are proved for (suitably defined) weak solutions. Some applications to P.D.E. are also given: they concern linear hyperbolic equations either in non-cylindrical regions or with mixed variable lateral conditions.

CONVERGENCE RESULTS FOR A PHASE TRANSITION MODEL WITH VANISHING MICROSCOPIC ACCELERATION

A recent phase transition model, proposed by Fremond, is based on the consideration that the microscopic movements are responsible for the phase transition at the macroscopic level. A last version of the model, accounting also for the microscopic accelerations has been investigated in Ref. 4, where well-posedness results are established for related Cauchy–Neumann problems. The aim of this paper is the study of the asymptotic behavior of the solution to one of the above problems, as the power of the microscopic acceleration forces goes to zero.

Global existence for a nonlocal model for adhesive contact

Abstract In this paper, we address the analytical investigation into a model for adhesive contact introduced in a paper by Freddi and Fremond, which includes nonlocal sources of damage on the contact surface, such as the elongation. The resulting PDE system features various nonlinearities rendering the unilateral contact conditions, the physical constraints on the internal variables, as well as the contributions related to the nonlocal forces. For the associated initial-boundary value problem, we obtain a global-in-time existence result by proving the existence of a local solution via a suitable approximation procedure and then by extending the local solution to a global one by a nonstandard prolongation argument.

Global well-posedness for a phase transition model with irreversible evolution and acceleration forces

In this paper we investigate a nonlinear PDE system describing irreversible phase transition phenomena where inertial effects are also included. Its derivation comes from the modelling approach proposed by M. Fremond. We obtain a global in time existence and uniqueness result for the related initial and boundary value problem.