Periodic Solutions and Torsional Instability in a Nonlinear Nonlocal Plate Equation
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Publication:5231334
DOI10.1137/18M1221242zbMath1437.35452arXiv1809.09783MaRDI QIDQ5231334
Denis Bonheure, Gazzola, Filippo, Ederson Moreira dos Santos
Publication date: 26 August 2019
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1809.09783
Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Periodic solutions to PDEs (35B10) Plates (74K20) Initial-boundary value problems for higher-order hyperbolic equations (35L35) Integro-partial differential equations (35R09) Higher-order semilinear hyperbolic equations (35L76)
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Cites Work
- A partially hinged rectangular plate as a model for suspension bridges
- Instability of modes in a partially hinged rectangular plate
- N-cyclic functions and multiple subharmonic solutions of Duffing's equation
- Nonlinear questions in clamped plate models
- On the justification of plate models
- An evolution von Kármán equation modeling suspension bridges
- Structural instability of nonlinear plates modelling suspension bridges: mathematical answers to some long-standing questions
- Nonlinear buckled states of rectangular plates
- Infinite-dimensional dynamical systems in mechanics and physics.
- An infinite dimensional Duffing-like evolution equation with linear dissipation and an asymptotically small source term
- Hinged and supported plates with corners
- Boundedness and stability for the damped and forced single well Duffing equation
- Torsional instability in suspension bridges: the Tacoma Narrows Bridge case
- Mathematical models for suspension bridges. Nonlinear structural instability
- A clamped plate with a uniform weight may change sign
- In any dimension a ``clamped plate with a uniform weight may change sign
- Bending and stretching energies in a rectangular plate modeling suspension bridges
- Initial-boundary value problems for an extensible beam
- On the variation of longitudinal and torsional frequencies in a partially hinged rectangular plate
- Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
- The Bending and Stretching of Plates
- The action of flexible bridges under wind, II: Buffeting theory
- Optimal uniqueness condition for the antiperiodic solutions of some nonlinear parabolic equations
- Nonlinear Vibrations and the Wave Equation
- Uniqueness and nonuniqueness results for the antiperiodic solutions of some second-order nonlinear evolution equations
- Modeling suspension bridges through the von Kármán quasilinear plate equations
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