8 papers
A nonlocal formulation for the problem of microwave heating of material with temperature dependent conductivity
Giovanni Cimatti
Microwave electromagnetic heating are widely used in many industrial processes. The mathematics involved is based on the Maxwell's equations coupled with the heat equation. The the…
Remark on the exponential decay of the solutions of the damped wave equation
Giovanni Cimatti
A condition which guaranties the exponential decay of the solutions of the initial-boundary value problem for the damped wave equation is proved. A method for the effective computa…
A variational principle for the system of P.D.E. of porous metal bearings
Giovanni Cimatti
Porous metal bearings are widely used in small and micro devices. To compute the pressure one has to solve the Reynolds equation coupled with the Laplace equation. We show that it…
The Maxwell-Volterra reciprocity law in electrodynamics
Giovanni Cimatti
Use is made of the theory of elliptic equations with measures data to prove the Maxwell-Volterra reciprocity law. A simple one-dimensional example is also given.
An hyperbolic system of P.D.E. relevant in general relativity
Giovanni Cimatti
Assuming as starting point the validity of the Einstein-Rosen metric, we study the hyperbolic system of P.D.E. to which the Einstein's field's equations can be reduced. We prove us…
Functional solutions for problems of heat and mass transfer
Giovanni Cimatti
We prove the existence and, in certain cases, the uniqueness of functional solutions for two boundary value problems of systems of P.D.E. in divergence form motivated by problems o…
An application of a theorem of G. Zwirner to a class of non-linear elliptic systems in divergence form
Giovanni Cimatti
A theorem on the solutions of the problem is applied for finding the functional solutions of the system of partial differential equatio…
Boundary value problems in general relativity
Giovanni Cimatti
Certain theorems of existence, non-existence and uniqueness for boundary value problems modelling axial symmetric problems in general relativity are presented using the Weyl's metr…