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Convergence to stationary solutions for a parabolic-hyperbolic phase-field system
Quasi-periodic solutions for 1D resonant beam equation
| 1. | School of Mathematical Sciences, Institute of Mathematics, Fudan University, Shanghai 200433, China |
| 2. | Department of Mathematics, Nanjing University, Nanjing 210093, China |
$u_{t t} +u_{x x x x} +u^3=0,$
with hinged boundary conditions is considered. It is proved that the above equation admits small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system. The proof is based on infinite dimensional KAM theorem, partial normal form and scaling skills.
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