Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres

@inproceedings{Delort2015QuasiLinearPO,
  title={Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres},
  author={Jean-Marc Delort},
  year={2015}
}
The Hamiltonian $\int_X(\abs{\partial_t u}^2 + \abs{\nabla u}^2 + \m^2\abs{u}^2)\,dx$, defined on functions on $\R\times X$, where $X$ is a compact manifold, has critical points which are solutions of the linear Klein-Gordon equation. We consider perturbations of this Hamiltonian, given by polynomial expressions depending on first order derivatives of $u$. The associated PDE is then a quasi-linear Klein-Gordon equation. We show that, when $X$ is the sphere, and when the mass parameter $\m$ is… 

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