Asymptotic behavior of solutions toward the rarefaction waves to the Cauchy problem for the generalized Benjamin–Bona–Mahony–Burgers equation with dissipative term

In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem with the far field condititon for the generalized Benjamin–Bona–Mahony–Burgers equation with a fourth-order dissipative term. When the corresponding Riemann problem for the hyperbolic part admits a Riemann solution which consists of single rarefaction wave, it is proved that the solution of the Cauchy problem tends toward the rarefaction wave as time goes to infinity. We can further obtain the same global asymptotic stability of the rarefaction wave to the generalized Korteweg–de Vries–Benjamin–Bona–Mahony–Burgers equation with a fourth-order dissipative term as the former one.

Non-equilibrium steady state formation in 3+1 dimensions

We present the first holographic simulations of non-equilibrium steady state formation in strongly coupled \mathcal{N}=4𝒩=4 SYM theory in 3+1 dimensions. We initially join together two thermal baths at different temperatures and chemical potentials and compare the subsequent evolution of the combined system to analytical solutions of the corresponding Riemann problem and to numerical solutions of ideal and viscous hydrodynamics. The time evolution of the energy density that we obtain holographically is consistent with the combination of a shock and a rarefaction wave: A shock wave moves towards the cold bath, and a smooth broadening wave towards the hot bath. Between the two waves emerges a steady state with constant temperature and flow velocity, both of which are accurately described by a shock+rarefaction wave solution of the Riemann problem. In the steady state region, a smooth crossover develops between two regions of different charge density. This is reminiscent of a contact discontinuity in the Riemann problem. We also obtain results for the entanglement entropy of regions crossed by shock and rarefaction waves and find both of them to closely follow the evolution of the energy density.

Asymptotic stability of rarefaction wave for the compressible Navier‐Stokes‐Korteweg equations in the half space

In this study, we are concerned with the asymptotic stability towards a rarefaction wave of the solution to an outflow problem for the Navier-Stokes Korteweg equations of a compressible fluid in the half space. We assume that the space-asymptotic states and the boundary data satisfy some conditions so that the time-asymptotic state of this solution is a rarefaction wave. Then we show that the rarefaction wave is non-linearly stable, as time goes to infinity, provided that the strength of the wave is weak and the initial perturbation is small. The proof is mainly based on $L^{2}$ -energy method and some time-decay estimates in $L^{p}$ -norm for the smoothed rarefaction wave.

The research for characters of detonated rupture disks used in rarefaction wave gun for test

In this paper, numerical and experimental analysis were carried out to study the characters of the detonated rupture disks used in rarefaction wave gun for test. The pressure bearing capacity and cutting blasting ability of the disks were studied in detail. The research results showed that the designed detonated rupture disks could withstand the maximum pressure of 140 MPa or more during launch process. The central detonating spoke had an annular cutting depth of about 1.3 mm. It was not the shearing deformation at the supporting edge but the excessive tensile deformation at the middle position that led to the failure. The disk was cut and destroyed as a whole satisfyingly, so the rationality and feasibility of the detonated rupture disks used in rarefaction wave gun for test were verified, which could provide a reference for the development of rarefaction wave artillery and similar low recoil weapons.