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| Author(s): |
Vanderley Alves Ferreira Junior
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2016-03-31 |
| Examining board members: |
Ederson Moreira dos Santos;
Marcelo Moreira Cavalcanti;
Lucas Catão de Freitas Ferreira;
Djairo Guedes de Figueiredo;
Ma To Fu
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| Advisor: | Ederson Moreira dos Santos |
| Abstract | |
Fourth order differential equations appear naturally when modeling oscillations in elastic structures such as those observed in suspension bridges. Two models describing oscillations in the roadway of a bridge are considered. In the one-dimensional model we study finite space blow up of solutions for a class of fourth order differential equations. The results answer a conjecture presented in [F. Gazzola and R. Pavani. Wide oscillation finite time blow up for solutions to nonlinear fourth order differential equations. Arch. Ration. Mech. Anal., 207(2):717752, 2013] and imply the nonexistence of beam oscillation given by traveling wave profile with low speed propagation. In the two-dimensional model we analyze a nonlocal equation for a thin narrow prestressed rectangular plate where the two short edges are hinged and the two long edges are free. We prove existence and uniqueness of weak solution and we study its asymptotic behavior under viscous damping. We also study the stability of simple modes of oscillations which are classified as longitudinal or torsional. (AU) | |
| FAPESP's process: | 12/23741-3 - Fourth order elliptic equations |
| Grantee: | Vanderley Alves Ferreira Junior |
| Support Opportunities: | Scholarships in Brazil - Doctorate |