On global existence of localized solutions of some nonlinear lattices

Abstract

We prove global existence and uniqueness of solutions of some important nonlinea lattices which include the Fermi-Pasta-Ularn (FPU) lattice. Our result shows (on a particular example) that the FPU lattice with high nonlinearity and its continuum limit display drastically different behaviour with respect to blow up phenomenon

AMS:

• 35A10

Keywords:

• Nonlinear lattices
• energy method
• high interaction

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Notes

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