GLOBAL CLASSICAL SOLUTIONS TO THE 3-D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL INITIAL ENERGY

We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ｜｜po｜｜L∞ is appropriate small and 1 〈 γ 〈 6/5. Here the initial density could have vacuum and we do not require that the initial energy is small.

BLOW-UP OF THE SOLUTION FOR A CLASS OF POROUS MEDIUM EQUATION WITH POSITIVE INITIAL ENERGY

This paper deals with a class of porous medium equation ut=△u^m＋f（u）with homogeneous Dirichlet boundary conditions. The blow-up criteria is established by using the method of energy under the suitable condition on the function f（u）.

Experimental research into the effect of gas pressure,particle size and nozzle area on initial gas-release energy during gas desorption

Coal and gas outburst is a violent disaster driven by released energy from gas desorption.The initial expansion energy of released gas(IEERG)is a new method to predict coal and gas outburst.In this paper,an instrument for IEERG measurement was developed.Compared with previous setups,the new one which is equipped with three convergent nozzles and quick-release mechanism gets improved in data acquisition and gas sealing and releasing performance.To comprehensively know the effect of gas pressure,particle size,and nozzle area on IEERG,a series of experiments were carried out with this new setup.The variable control test results indicated that the gas pressure-IEERG curves remain the linear trend and the particle size-IEERG curves maintain the negative exponential trend for nozzle areas at 1.13,2.26,and3.39 mm2,respectively.The increase in nozzle area leads to deceases in value of IEERG and absolute value of slope of fitting curves in each test.In addition,the orthogonal experiment showed that the influence of gas pressure,nozzle area,and particle size on IEERG decreases in turn.Only gas pressure had a marked impact on IEERG.This work offers great importance in improving the accuracy of prediction of coal and gas outburst.

Exponential Growth of Solutions for Nonlinear Coupled Viscoelastic Wave Equations with Degenerate Nonlocal Damping and Source Terms

This paper is concerned with a system of nonlinear viscoelastic wave equations with degenerate nonlocal damping and memory terms.We will prove that the energy associated to the system is unbounded.In fact,it will be proved that the energy will grow up as an exponential function as time goes to infinity,provided that the initial data are positive initial energy.

Asymptotic Property of Solutions in a 4th-Order Parabolic Model for Epitaxial Growth of Thin Film

This paper deals with a homogeneous Neumann initial-boundary problem of a 4th-order parabolic equation modeling epitaxial growth of thin film. We determine the classification of initial energy on the existence of blow-up, global existence and extinction of solutions by using the potential well method and the auxiliary function method.Moreover, asymptotic estimates on global solution and extinction solution are studied,respectively.

Experimental study on detonation parameters and cellular structures of fuel cloud

In this paper, detonation parameters of fuel cloud, such as propylene oxide （PO）, isopropyl nitrate （IPN）, hex- ane, 90# oil and decane were measured in a self-designed and constructed vertical shock tube. Results show that the deto- nation pressure and velocity of PO increase to a peak value and then decrease smoothly with increasing equivalence ra- tio. Several nitrate sensitizers were added into PO to make fuel mixtures, and test results indicated that the additives can efficiently enhance detonation velocity and pressure of fuel cloud and one type of additive n-propyl nitrate （NPN） played the best in the improvement. The critical initiation energy that directly initiated detonation of all the test liquid fuel clouds showed a U-shape curve relationship with equiva- lence ratios. The optimum concentration lies on the rich-fuel side （;b 〉 1）. The critical initiation energy is closely related to molecular structure and volatility of fuels. IPN and PO have similar critical values while that of alkanes are larger. Detonation cell sizes of PO were respectively investigated at 25;C, 35;C and 50;C with smoked foil technique. The cell width shows a U-shape curve relationship with equivalence ratios at all temperatures. The minimal cell width also lies on the rich-fuel side （;b 〉 1）. The cell width of PO vapor is slightly larger than that of PO cloud. Therefore, the deto- nation reaction of PO at normal temperature is controlled by gas phase reaction.

Theoretical prediction of the optimal conditions for observing the stereodynamical vector properties of the C(~3P) + OH(X^2Π) → CO(X^1 Σ^+) + H(~2S) reaction

The best optimal initial reactant state and collision energy for observing the stereodynamical vector properties of the title reaction in the ground electronic state X2A’ potential energy surface （PES）[Zanchet et al. 2006 J. Phys. Chem. A 110 12017] are theoretically predicted using the quasi-classical trajectory （QCT） method for the first time. The calculated results reveal that the smallest value of the rotational quantum number j, larger vibrational quantum number v, and the lower strength of collision energy should be selected for offering the most obvious picture about the stereodynamical vector properties. Polarization-dependent differential cross sections and the angular momentum alignment distribution, P（θr） and P（Φr） in the center-of-mass frame, are obtained to gain an insight into the alignment and orientation of the product molecules. The rotational angular momentum vector j’ of CO is aligned to be perpendicular to reagent relative velocity k. The product polarizations align along the y axis, pointing to the positive direction of the y axis. A new method is developed to investigate massive reactions with various initial states and to further study the vector properties of the fundamental reactions in detail.

Remarks on Blow-Up Phenomena in p-Laplacian Heat Equation with Inhomogeneous Nonlinearity

We investigate the p-Laplace heat equation ut-△_(p)u=ζ(t)f(u)in a bounded smooth domain.Using differential-inequality arguments,we prove blow-up results under suitable conditions onζ,f,and the initial datum u_(0).We also give an upper bound for the blow-up time in each case.