European Journal of Applied Mathematics

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The effect of hydrodynamic dispersion on reactive flows in porous media
European Journal of Applied Mathematics - Tập 12 Số 5 - Trang 557-569 - 2001
John Chadam, P. Ortoleva, Yongming Qin, R. STAMICAR
The shape stability of the reaction interface for reactive flow in a porous medium is investigated. Previous work showed that the Reaction-Infiltration Instability could cause the reaction zone to lose stability when the Peclet number exceeded a critical value. The new feature of this study is to include a velocity-dependent hydrodynamic dispersion. A mathematical model for this phenom...... hiện toàn bộ
On the dynamic behaviour of a thermoviscoelastic body in frictional contact with a rigid obstacle
European Journal of Applied Mathematics - Tập 8 Số 4 - Trang 417-436 - 1997
Kevin T. Andrews, K.L. Kuttler, Meir Shillor
We consider the dynamic behaviour of a thermoviscoelastic body which may come into frictional contact with a rigid obstacle. The frictional contact is modelled by general contact and friction laws which include as special cases the power law normal compliance condition and the corresponding generalization of Coulomb's law of dry friction. The stress-strain constitutive rela...... hiện toàn bộ
Convergence of the phase field model to its sharp interface limits
European Journal of Applied Mathematics - Tập 9 Số 4 - Trang 417-445 - 1998
Gunduz Caginalp, Xinfu Chen
We consider the distinguished limits of the phase field equations and prove that the corresponding free boundary problem is attained in each case. These include the classical Stefan model, the surface tension model (with or without kinetics), the surface tension model with zero specific heat, the two phase Hele–Shaw, or quasi-static, model. The Hele–Shaw model is also a limit of the...... hiện toàn bộ
Models for thin viscous sheets
European Journal of Applied Mathematics - Tập 7 Số 4 - Trang 321-343 - 1996
P. D. Howell
Leading-order equations governing the dynamics of a two-dimensional thin viscous sheet are derived. The inclusion of inertia effects is found to result in an ill-posed model when the sheet is compressed, and the resulting paradox is resolved by rescaling the equations over new length-and timescales which depend on the Reynolds number of the flow and the aspect ratio of the sheet. Physicall...... hiện toàn bộ
Stability of standing waves for a class of quasilinear Schrödinger equations
European Journal of Applied Mathematics - Tập 23 Số 5 - Trang 611-633 - 2012
Jianqing Chen, Yongqing Li, Zhi-Qiang Wang
This paper is concerned with the stability and instability of standing waves for the quasilinear Schrödinger equation of the form which has been derived in many models from mathematical physics. We find the exact threshold depending upon the interplay of quasilinear and nonlinear terms that separates stability and instability. More precisely, we prove that for α ∈ and odd p ∈ , when $1 < p < 4\alpha -1 +{4\over N}$, the standing wave is stable, and when hiện toàn bộ
The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part I: Mathematical analysis
European Journal of Applied Mathematics - Tập 2 Số 3 - Trang 233-280 - 1991
James F. Blowey, Charles M. Elliott
A mathematical analysis is carried out for the Cahn–Hilliard equation where the free energy takes the form of a double well potential function with infinite walls. Existence and uniqueness are proved for a weak formulation of the problem which possesses a Lyapunov functional. Regularity results are presented for the weak formulation, and consideration is given to the asymptotic behaviour a...... hiện toàn bộ
Analytical models of water impact
European Journal of Applied Mathematics - Tập 15 Số 6 - Trang 821-838 - 2004
A.A. Korobkin
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