Marco Luigi Bernardi

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.

Optimal control problems of phase relaxation models

This work is concerned with optimal control problems with convex cost criterion governed by the relaxed Stefan problem with or without memory. The existence of an optimal control is proved and necessary conditions for a given function to be an optimal control are found. Moreover, an asymptotic analysis is performed as the time relaxation parameter tends to zero.

A mathematical model for the evolution of cell populations under the action of mutagenic agents

Abstract The evolution of a homogeneous cell population under the action of mutagenic agents is investigated and account taken of the reversible character of genetic damage and the cell replication cycle. A mathematical model is obtained and consists of a system of first order partial differential equations.

Second order abstract differential equations with singular coefficients

SummaryWe study a large class of second order linear abstract differential equations, whose coefficients can be singular. In the framework of suitable « weighted » spaces, we prove some existence and uniqueness results for generalized and ordinary solutions of initial value problems for such equations.

On a differential problem coming from cell biology

SummaryAn initial and boundary value problem for a system of first order linear partial differential equations is studied. This problem arises in cell biology, when the evolution of a homogeneous cell population is modelled. Some existence, uniqueness and regularity results are proven; an estimate for the growth of the cell population is also obtained.

On a Mathematical Problem Arising in Cell Population Biology

We present some results concerning an initial and boundary value problem for a system of first order linear partial differential equations. This problem comes from modelling the evolution of a homogeneous cell population, where the cells may replicate and are. submitted to the action of some mutagenic agent.