DISPERSIVE SHOCKS IN DIFFUSIVE-DISPERSIVE APPROXIMATIONS OF ELASTICITY AND QUANTUM-HYDRODYNAMICS

Daria Bolbot, Dimitrios Mitsotakis, Athanasios Tzavaras

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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.
Original languageEnglish (US)
JournalQUARTERLY OF APPLIED MATHEMATICS
DOIs
StatePublished - Feb 17 2023

Bibliographical note

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.

Fingerprint

Dive into the research topics of 'DISPERSIVE SHOCKS IN DIFFUSIVE-DISPERSIVE APPROXIMATIONS OF ELASTICITY AND QUANTUM-HYDRODYNAMICS'. Together they form a unique fingerprint.

Cite this