Singular shock waves in interactions

Singular Shock Waves in Interactions

In a number of papers it was shown that there are one-dimensional systems such that they contain solutions with, so called, overcompressive singular shock waves besides the usual elementary waves (shock and rarefaction ones as well as contact discontinuities). One can see their definition for a general 2 × 2 system with fluxes linear in one of dependent variables in [8]. This paper is devoted t...

Shadow Waves – Entropies and Interactions for Delta and Singular Shocks

The paper deal with two key problems for delta (or singular) shock solutions to systems of conservation laws: entropy admissibility conditions for them (which is connected to the notorious uniqueness problem) and their interaction. A way we chose is to represent them by nets of piecewise constant (or constant with respect only to the space variable) functions, here called shadow waves. All the ...

Solitary Waves, Shock Waves and Singular Solitons of the Generalized Ostrovsky-Benjamin-Bona-Mahoney Equation

This paper obtains the solitary wave, shock wave as well as singular soliton solutions to the generalized OstrovskyBenjamin-Bona-Mahoney (gO-BBM) equation. The ansatz method is applied to obtain the solutions. Several constraint conditions for the parameters are derived that establish the existence of the soliton solutions.

Shock Waves in Liquid

Asbtract The structure of shock waves in liquids containing gas bubbles is investigated theoretically. The mechanisms taken into account are the steepening of compression waves in the mixture by convection and the effects due to the motion of the bubbles with respect to the surrounding fluid. This relative motion, radial and translational, gives rise to dissipation and to dispersion caused by t...

Shock Waves in Medicine