Giovanni Cimatti

On a problem of the theory of lubrication governed by a variational inequality

The hydrodynamic lubrication of a complete journal bearing of finite width is studied using the theory of variational inequalities: we deal mainly with existence, uniqueness and regularity of the solution.

Existence results for a nonlinear elliptic system modelling a temperature dependent electrical resistor

SummaryThe electrical resistance in many substances varies greatly with the temperature which in turns depends on the Joule effect. This nonlinear effect is described under steady conditions by a system of nonlinear elliptic equations with a quadratic growth in the gradient. This work gives a theorem of existence for the related elliptic boundary value problem.

Existence of Weak Solutions for the Nonstationary Problem of the Joule Heating of a Conductor (

SummaryAn initial-boundary value problem for a system of two nonlinear partial differential equations is studied using the Faedo-Galerkin method. The problem describes the electric heating of a conducting body. The main result is a theorem of existence of weak solutions for an arbitrarily large interval of time.

The stationary thermistor problem with a current limiting device

The electrical heating of a conductor connected with a current limiting device of total resistance R is studied under mixed boundary conditions. A theorem of existence is given using a transformation which permits the reduction of the nonlinear system governing the problem to the classical mixed boundary value problem for the Laplace equation

How the Reynolds equation is related to the Stokes equations

The Reynolds equation, which gives the pressure distribution in a thin layer of lubricating fluid, is usually motivated in a rather heuristic way. We make an attempt to clarify how the Reynolds equation can be viewed as an asymptotic solution of the Stokes equations.

Existence and uniqueness for nonlinear reynolds equations

Abstract The pressure distribution in a gas-lubricated bearing is given by the nonlinear Reynolds equation with the boundary value problem ▽ · ( H 3 P ▽ P ) = Λ ( HP ) x in Ω, P = G on δω. Various results of existence and uniqueness for this equation are presented. Furthermore the system of nonlinear equations arising when elastic deformation of the bearing surfaces is not neglected is discussed.

Existence and uniqueness for the equations of the joule-thomson effect

The electrical heating of a conductor obeying the Wiedemann-Pranz law is studied taking into account the Thomsons effect. Using a suitable transformation, the nonlinear elliptic system governing the problem is put in divergence form. The new formulation permits to find a bound for the temperature, to prove a theorem of existence and, in a special case, a result of uniqueness

On Certain Nonlinear Problems Arising in the Theory of Lubrication

Various nonlinear elliptic boundary value problems motivated by the theory of lubrication are stated and studied. We deal mainly with the aspects of existence and uniqueness of solutions.

On some singular perturbation problems in the theory of lubrication

Some singular perturbation problems occurring in the theory of hydrodynamic lubrication are studied. We examine in detail the case of the very long or very short journal bearing; the asymptotic problem of small eccentricity ratio is also considered.

On the numerical solution of a variational inequality connected with the hydrodynamic lubrication of a complete journal bearing

The theory of variational inequalities is applied to a problem of lubrication. A method for solving numerically the relevant variational inequality is presented.