Marco Pozza
Published 2023-03-07, updated 2023-06-27Version 2
Starting from Namah and Roquejoffre (1999) and Fathi (1998), the large time asymptotic behavior of solutions to Hamilton--Jacobi equations has been extensively investigated by many authors, mostly on smooth compact manifolds and the flat torus. We extend it to the case where the ambient space is a network. For the well posedness of time dependent problems on networks, the equation must be coupled with a "flux limiter", that is the choice of appropriate constants on each vertex of the network. We will investigate the effects of it on the asymptotic analysis.
The selection problem for a new class of perturbations of Hamilton-Jacobi equations and its applications
Convergence of solutions of Hamilton-Jacobi equations depending nonlinearly on the unknown function
Large time behavior of the solutions to the difference wave operators
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