Fronts in dissipative Fermi-Pasta-Ulam-Tsingou chains

Abstract

In a dissipative Fermi-Pasta-Ulam-Tsingou chain particles interact with their nearest neighbors through anharmonic potentials and linear dissipative forces. We prove the existence of front solutions connecting two different uniformly compressed (or stretched) states at $\pm \infty$ using an implicit function argument starting at a suitable continuum limit in the case of large damping. A detailed analysis allows us to show monotonicity of waves and to determine sharp exponential decay rates for a wide class of potentials including Hertzian potentials.

26 pages

References in corpus (11)

• Angle of Repose and Angle of Marginal Stability: Molecular Dyanmics of Granular Particles
• Shock Wave Structure in a Strongly Nonlinear Granular Lattice with Viscous Dissipation
• Riemann solvers and undercompressive shocks of convex FPU chains
• Gaussian solitary waves and compactons in Fermi-Pasta-Ulam lattices with Hertzian potentials
• On the existence of solitary traveling waves for generalized Hertzian chains
• Unimodal wave trains and solitons in convex FPU chains
• Heteroclinic travelling waves in convex FPU-type chains
• Shock waves in the dissipative Toda lattice
• Asymptotic formulas for solitary waves in the high-energy limit of FPU-type chains
• Subsonic phase transition waves in bistable lattice models with small spinodal region
• Action minimizing fronts in general FPU-type chains