Quasi Linear Perturbations of Hamiltonian Klein Gordon Equations on Spheres is popular PDF and ePub book, written by J.-M. Delort in 2015-02-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Quasi Linear Perturbations of Hamiltonian Klein Gordon Equations on Spheres can be Read Online from any device for your convenience.
Quasi Linear Perturbations of Hamiltonian Klein Gordon Equations on Spheres Book PDF Summary
The Hamiltonian ∫X(∣∂tu∣2+∣∇u∣2+m2∣u∣2)dx, defined on functions on R×X, where X is a compact manifold, has critical points which are solutions of the linear Klein-Gordon equation. The author considers 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. The author shows that, when X is the sphere, and when the mass parameter m is outside an exceptional subset of zero measure, smooth Cauchy data of small size ϵ give rise to almost global solutions, i.e. solutions defined on a time interval of length cNϵ−N for any N. Previous results were limited either to the semi-linear case (when the perturbation of the Hamiltonian depends only on u) or to the one dimensional problem. The proof is based on a quasi-linear version of the Birkhoff normal forms method, relying on convenient generalizations of para-differential calculus.
Detail Book of Quasi Linear Perturbations of Hamiltonian Klein Gordon Equations on Spheres PDF
- Author : J.-M. Delort
- Release : 06 February 2015
- Publisher : American Mathematical Soc.
- ISBN : 9781470409838
- Genre : Mathematics
- Total Page : 92 pages
- Language : English
- PDF File Size : 19,8 Mb
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