Shock capturing and related numerical methods in computational fluid dynamics.
Shock fluctuations in a particle system
Shock waves and general relativity
Shock waves in gas dynamics.
Shock-wave explosions in general relativity
Singular solutions to systems of conservation laws and their algebraic aspects
We discuss the definitions of singular solutions (in the form of integral identities) to systems of conservation laws such as shocks, δ-, δ’-, and -shocks (n = 2,3,...). Using these definitions, the Rankine-Hugoniot conditions for δ- and δ’-shocks are derived. The weak asymptotics method for the solution of the Cauchy problems admitting δ- and δ’-shocks is briefly described. The algebraic aspects of such singular solutions are studied. Namely, explicit formulas for flux-functions of singular solutions...
Some remarks on conservative symmetric-hyperbolic systems governing relativistic theories
Spectral stability of undercompressive shock profile solutions of a modified KdV-Burgers equation.
Stability of shock waves in relativistic radiation hydrodynamics
Stability of strong detonation waves and rates of convergence.
Sur la construction des solutions approchées d'un problème de tsunami