Asymptotic Analysis - Volume 24, issue 1

Authors: Jecko, Th.

Article Type: Research Article

Abstract: [fr] Pour des molécules diatomiques dans la limite de Born–Oppenheimer, on construit une approximation adiabatique de plusieurs sections efficaces totales, y compris des sections inélastiques. On montre la prépondérance de la diffusion élastique et l’on en donne des termes dominants. L’un d’eux contient un potentiel effectif, ce qui permet de réduire la diffusion à celle d’un système à deux corps. De plus, l’approximation améliore une borne a priori sur d’autres sections totales. Abstract. In the Born–Oppenheimer limit, for diatomic molecules, we approximate several total cross‐sections, including inelastic ones, by adiabatic equivalents. We show the preponderance of the elastic total …cross‐section and we give leading terms for it. One of them contains a two‐body efficient potential so that the scattering behaviour may be well‐approximated by those of some two‐body system. Furthermore, the adiabatic approximation improves an a priori bound on some other total cross‐sections. Show more

Citation: Asymptotic Analysis, vol. 24, no. 1, pp. 1-35, 2000

Authors: Chasseigne, Emmanuel

Article Type: Research Article

Abstract: We consider the following non linear diffusion equation with critical absorption exponent: u_{t}-\Delta u^{m}+u^{m}=0 , m>1 , in a bounded set \varOmega and in \mathbb{R}^{N} . In the whole space, we give optimal conditions on measure initial data to have existence and uniqueness, and we study singular solutions, which explode in \varOmega when t\rightarrow0 . The problem of the initial trace is also completely addressed, and we derive estimates for the initial trace of continuous solutions.

Citation: Asymptotic Analysis, vol. 24, no. 1, pp. 37-72, 2000

Authors: Brezis, H. | Kamin, S. | Sivashinsky, G.

Article Type: Research Article

Abstract: The long‐time behavior of the solution of the system \theta_\tau - \alpha \pi_\tau = \varOmega (\theta) , \pi_\tau - \theta_\tau = \pi_{\xi\xi} is investigated. Such a system is related to the modeling of detonation waves subjected to strong hydraulic resistance. We establish that some initial conditions yield decay (failure of ignition) while for other initial conditions our results strongly suggest convergence to traveling waves (successful ignition).

Citation: Asymptotic Analysis, vol. 24, no. 1, pp. 73-90, 2000