TY - JOUR
T1 - DISPERSIVE SHOCKS IN DIFFUSIVE-DISPERSIVE APPROXIMATIONS OF ELASTICITY AND QUANTUM-HYDRODYNAMICS
AU - Bolbot, Daria
AU - Mitsotakis, Dimitrios
AU - Tzavaras, Athanasios
N1 - KAUST Repository Item: Exported on 2023-03-17
Acknowledgements: The second author thanks KAUST for their hospitality during a visit when this work was initiated.
PY - 2023/2/17
Y1 - 2023/2/17
N2 - The aim is to assess the combined effect of diffusion and dispersion on shocks in the moderate dispersion regime. For a diffusive dispersive approximation of the equations of one-dimensional elasticity (or p-system), we study convergence of traveling waves to shocks. The problem is recast as a Hamiltonian system with small friction, and an analysis of the length of oscillations yields convergence in the moderate dispersion regime ε, δ → 0 with δ = o(ε), under hypotheses that the limiting shock is admissible according to the Liu E-condition and is not a contact discontinuity at either end state. A similar convergence result is proved for traveling waves of the quantum hydrodynamic system with artificial viscosity as well as for a viscous Peregrine-Boussinesq system where traveling waves model undular bores, in all cases in the moderate dispersion regime.
AB - The aim is to assess the combined effect of diffusion and dispersion on shocks in the moderate dispersion regime. For a diffusive dispersive approximation of the equations of one-dimensional elasticity (or p-system), we study convergence of traveling waves to shocks. The problem is recast as a Hamiltonian system with small friction, and an analysis of the length of oscillations yields convergence in the moderate dispersion regime ε, δ → 0 with δ = o(ε), under hypotheses that the limiting shock is admissible according to the Liu E-condition and is not a contact discontinuity at either end state. A similar convergence result is proved for traveling waves of the quantum hydrodynamic system with artificial viscosity as well as for a viscous Peregrine-Boussinesq system where traveling waves model undular bores, in all cases in the moderate dispersion regime.
UR - http://hdl.handle.net/10754/686743
UR - https://www.ams.org/qam/0000-000-00/S0033-569X-2023-01658-X/
U2 - 10.1090/qam/1658
DO - 10.1090/qam/1658
M3 - Article
SN - 1552-4485
JO - QUARTERLY OF APPLIED MATHEMATICS
JF - QUARTERLY OF APPLIED MATHEMATICS
ER -