Homogenization of Hamilton–Jacobi equations on networks
speaker: Antonio Siconolfi (Università di Roma La Sapienza)abstract: We present an homogenization procedure for time dependent Hamilton–Jacobi equations posed on networks embedded in the Euclidean space R
N , and depending on an oscillation parameter ε
which becomes infinitesimal. The peculiarity of the construction is that the limit equation is posed in an Euclidean space whose dimension depends on the topological complexity of the network. Approximating and limit equations are therefore defined on different spaces, this requires an appropriate notion of convergence for the corresponding solutions. We use closed probability measures defined on an abstract graph underlying the network, and define an equivalent on graph of the so–called Mather α and β functions. The α function plays the role of effective Hamiltonian. The results have been obtained in collaboration with Marco Pozza and Alfonso Sorrentino.
timetable:
Tue 9 May, 10:10 - 10:40, Aula Dini
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