Seminar

A generalization of the discrete Lagrange model of the vibrating string to the case of dimension > 1 of the spatial variable

4 November 2022
Start time 
10:00 am
Polo Ferrari 1 - Via Sommarive 5, Povo (Trento)
Room A211
Organizer: 
Dipartimento di Matematica
Target audience: 
University community
Attendance: 
Free
Contact person: 
Prof. Marco Sabatini
Contact details: 
Staff Dipartimento di Matematica
Speaker: 
Massimo Villarini (UniMORE - Università di Modena e Reggio Emilia)

Abstract:

A celebrated theorem of Lagrange  defines a discrete model, only based on Newton's Second Law of dynamics, for the PDE describing the transversal motion of a string: such mechanicaI  model is expressed through a family of second order ODEs, depending on a discretization parameter, whose solutions Lagrange proved to converge uniformly to the solutions of the PDE, as the discretization parameter tends to 0.  Answering to a question posed by Gallavotti,  we generalize this theorem to the case of n-dimensional space variable, n>1.