Stability of traveling wave fronts for nonlocal diffusive systems

This paper is concerned with stability of traveling wave fronts for nonlocal diffusive sys­tem.We adopt L^(1),-weighted,L^(1)-and L^(2)-energy estimates for the perturbation systems,and show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave fronts provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev spaces.

ON THE MINIMAL WAVE SPEED OF WAVE FRONTS FOR REACTION-DIFFUSION EQUATIONS

In this paper, a variational description of the minimal wave speed c(m, f) of wave fronts forthe reaction diffusion equations u_t=u_(xx)+u^mf(u) is given, where m>1 and f(u)～1-u.The continuity of c(m, f) in m and f is also proved. Especially, for f(u)=1-u, the estimateof the minimal wave speed c(m, f) is obtained.

Stochastic seismic wave interaction with a rock joint having Coulomb-slip behavior

Seismic wave interaction with a slippery rock joint with an arbitrary impinging angle is analytically studied based on the conservation of momentum on the wave fronts. Based on the displacement discontinuity method, the wave propagation equations are derived for incident P- and S-waves. By comparison, the calculated transmission and reflection coefficients for normal incident waves are the same as the existing results, which proves the wave propagation equation obtained in the paper is correct. The wave propagation derived in the context can be applied to incident waves with different waveforms. Stochastic seismic waves are then used to analyze the seismic wave interaction with the slippery rock joint, where the stochastic seismic waves are generated from frequency spectra. The parametric studies are carried out to investigate the effect of type, intensity and impinging angle of the incident seismic waves on the wave propagation across the slippery rock joint.

Finite Travelling Wave Solutions for a Semilinear System of Parabolic Type

Aict f Finjte rmvedrig wave (M) so1uhons fOr the fOllowhg sechear syttem (I){u_t-u_(xx)+u^mv^p=0 u_t-v_(xx)+u^q=0 -∞<x<+∞,t>0,p,q>0,m≥0 are studied. SolutiOns to (I) of the fOrm u (x, t)=lt(ct--x), v(x, t)=v (cl--X) are called W soIutiOns if there exjstS a fwite ', such that u({)=v(j)=0 for t<{,':=ct--x. It is proVed that if Pq+nl<l, fOr any ed c thele erktS an FTW that is inhque up to phase transIahons and Is unbOunded, whena no rm ekist if pq+m> l. The asmpptohc weve profileS near the front as well as far from it are also determined. If I)q^m = l. the exjstence of travebe wave soluhons to (I) is proved. The plnof in Esqniruis's paper(1990) for the one m=0 co be sdriplified by using the methOd develOped in thjs paper.

Detonation Shock Dynamics Relations for RDX-TNT Based Cast Explosives

RDX and TNT based explosives are very useful in performing research and development works especially when complex shaping of an assembly is required due to their molding capability and the range of ratios in which they can be mixed. In this paper, for these compositions, detonation shock dynamics （DSD） relations between normal detonation velocity D. and detonation wave curvature κ are determined for RDX： TNT explosives in weight ratios 40：60, 50：50 and 60：40. Experiments are performed with 50 mm diameter rate sticks of approximately 200 mm length using high speed rotating mirror camera and time measurement probes. The results show that first order DSD relation is indeed representative of these explosives. The slope of this relation increases by increasing TNT contents in these explosives. Going from 40% to 60% TNT, the data show an increase of more than 100% in negative slope of Dn-κ relation.

Travelling Wave Solutions in Delayed Reaction Diffusion Systems with Partial Monotonicity

This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of ＂desirable pair of upper-lower solutions＂, through which a subset can be constructed. We then apply the Schauder＇s fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts.

Stability of planar waves in reaction-diffusion system

This paper is concerned with the asymptotic stability of planar waves in reaction-diffusion system on Rn, where n 2. Under initial perturbation that decays at space infinity, the perturbed solution converges to planar waves as t →∞. The convergence is uniform in Rn. Moreover, the stability of planar waves in reaction-diffusion equations with nonlocal delays is also established by transforming the delayed equations into a non-delayed reaction-diffusion system.

TransientWaves Due to Mechanical Loads in Elasto-Thermo-Diffusive Solids

This paper deals with the study of transient waves in a homogeneous isotropic,solid halfspace with a permeating substance in the context of the theory of generalized elasto-thermodiffusion.The halfspace is assumed to be disturbed due to mechanical loads acting on its boundary.The model comprising of basic governing differential equations and boundary conditions has been solved by employing Laplace transform technique.Noting that the second sound effects are short lived,the small time approximations of solution for various physical quantities have been obtained and the results are discussed on the possible wave fronts.In case of continuous and periodic loads acting at the boundary,the displacement is found to be continuous at each wave front while it is discontinuous in case of impulsive load.The temperature and concentration fields are found to be discontinuous at all the wave fronts.The displacement,temperature change and concentration deviation due to impulsive,continuous and periodic mechanical loads have also been evaluated in the physical domain at all times by employing numerical inversion technique of integral transform.The computer simulated numerical results have been presented graphically in respect of displacement,temperature change and concentration deviation for brass.A significant effect of mass diffusion has been observed on the behaviour of mechanical and thermal waves.

ENTIRE SOLUTIONS FOR LOTKA-VOLTERRA COMPETITION-DIFFUSION MODEL

This paper is concerned with the existence of entire solutions of Lotka Volterra competition-diffusion model. Using the comparing argument and sub-super solutions method, we obtain the existence of entire solutions which behave as two wave fronts coming from the both sides of x-axis, where an entire solution is meant by a classical solution defined for all space and time variables.

TRAVELLING FRONT SOLUTIONS IN A DIFFUSIVE VECTOR DISEASE MODEL WITH SPATIO-TEMPORAL DELAY

This paper is concerned with travelling front solutions to a vector disease model with a spatio-temporal delay incorporated as an integral convolution over all the past time up to now and the whole one-dimensional spatial domain R.When the delay kernel is assumed to be the strong generic kernel,using the linear chain techniques and the geometric singular perturbation theory,the existence of travelling front solutions is shown for small delay.