REMARKS ON THE CAUCHY PROBLEM OF THE ONE-DIMENSIONAL VISCOUS RADIATIVE AND REACTIVE GAS

This paper is concerned with the large-time behavior of solutions to the Cauchy problem of a one-dimensional viscous radiative and reactive gas.Based on the elaborate energy estimates,we develop a new approach to derive the upper bound of the absolute temperature by avoiding the use of auxiliary functions Z(t)and W(t)introduced by Liao and Zhao[J.Differential Equations,2018,265(5):2076-2120].Our results also improve upon the results obtained in Liao and Zhao[J.Differential Equations,2018,265(5):2076-2120].

Solidification Behavior of in situ TiB_(2)/Cu Composite Powders during Reactive Gas Atomization

2wt%TiB_(2)/Cu composite powders were fabricated in situ by reactive gas atomization.The fabricated composite powder exhibits high sphericity,and the powder sizes range from 5μm to 150μm.The morphology of the Cu matrix and the distribution of the TiB2 particles in the composite powders vary with the powder size.The critical transitions of interface morphologies from dendritic-to-cellular and cellular-to-planar interfaces occurs when the composite powder sizes decrease to 34μm and 14μm,respectively.Compared with pure Cu droplets,the composite droplets undergo critical transition of the interface morphologies at a smaller droplet size corresponding to a higher cooling rate because the existence of TiB2 particles can cause instability in the advancing solidification front and heterogeneous nucleation.With decreasing powder size,the extent of the TiB_(2) particle interdendritic segregation decreases as the result of enhanced engulfment of TiB2 particles by the advancing solidification front.

Nonlinear stability of rarefaction waves for a viscous radiative and reactive gas with large initial perturbation

We investigate the time-asymptotically nonlinear stability of rarefaction waves to the Cauchy problem of a one-dimensional compressible Navier-Stokes type system for a viscous,compressible,radiative and reactive gas,where the constitutive relations for the pressure p,the speci c internal energy e,the speci c volume v,the absolute temperature θ,and the specific entropy s are given by p=Rθv+aθ^(4)/3,e=C_(v)θ+avθ^(4),and s=C_(v)lnθ+4avθ^(3)/3+Rln v with R>0,C_(v)>0 and a>0 being the perfect gas constant,the speci c heat and the radiation constant,respectively.For such a specific gas motion,a somewhat surprising fact is that,generally speaking,the pressure p(v,s)is not a convex function of the specific volume v and the specific entropy s.Even so,we show in this paper that the rarefaction waves are time-asymptotically stable for large initial perturbation provided that the radiation constant a and the strength of the rarefaction waves are sufficiently small.The key point in our analysis is to deduce the positive lower and upper bounds on the specific volume and the absolute temperature,which are uniform with respect to the space and the time variables,but are independent of the radiation constant a.

Blow-up of Viscous Compressible Reactive Self-gravitating Gas

In this paper, we prove some results concerning blow-up of viscous compressible reactive （selfgravitating） flows when the initial density is compactly supported and the other initial value satisfy proper conditions. It extends the work of Xin and Cho to the case of viscous compressible reactive self-gravitating flows equations. We control the lower bound of second moment by total energy and obtain the precise relationship between the size of the support of initial density and the existence time.

Unique Solvability for a Class of Non-newtonian Fluids for a Reacting Mixture with Vacuum

In this paper,we consider a class of non-Newtonian fluids for a reacting mixture in one-dimensional bounded interval, provided the initial data satisfying a compatibility condition. The main ingredient is that we allow the initial density vacuum.