Bonafini, Mauro (2019) Variational and convex approximations of 1-dimensional optimal networks and hyperbolic obstacle problems. PhD thesis, University of Trento.
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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)|
|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|
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