Bonafini, Mauro (2019) Variational and convex approximations of 1-dimensional optimal networks and hyperbolic obstacle problems. PhD thesis, University of Trento.
| PDF (PhD thesis) - Doctoral Thesis 7Mb | |
PDF - Disclaimer Restricted to Repository staff only until 9999. 136Kb |
Abstract
In this thesis we investigate variational problems involving 1-dimensional sets (e.g., curves, networks) and variational inequalities related to obstacle-type dynamics from a twofold prospective. On one side, we provide variational approximations and convex relaxations of the relevant energies and dynamics, moving mainly within the framework of Gamma-convergence and of convex analysis. On the other side, we thoroughly investigate the numerical optimization of the corresponding approximating energies, both to recover optimal 1-dimensional structures and to accurately simulate the actual dynamics.
Item Type: | Doctoral Thesis (PhD) |
---|---|
Doctoral School: | Mathematics |
PhD Cycle: | 31 |
Subjects: | Area 01 - Scienze matematiche e informatiche > MAT/05 ANALISI MATEMATICA Area 01 - Scienze matematiche e informatiche > MAT/08 ANALISI NUMERICA |
Repository Staff approval on: | 15 Apr 2019 10:02 |
Repository Staff Only: item control page