Showing papers in "Ima Journal of Applied Mathematics in 1986"
267 citations
TL;DR: In this paper, a nonlinear model of such interaction is developed and morphological instability of a planar dissolution front is demonstrated using a linear stability analysis of a moving-free-boundary problem.
Abstract: When a fluid flow is imposed on a porous medium, the infiltration flow may interact with the reaction-induced porosity variations within the medium and may lead to fingering instabilities. A nonlinear model of such interaction is developed and morphological instability of a planar dissolution front is demonstrated using a linear stability analysis of a moving-free-boundary problem. The fully nonlinear model is also examined numerically using finite-difference methods. The numerical simulations confirm the predictions of linear stability theory and, more importantly, reveal the growth of dissolution fingers that emerge as a result of these instabilities.
229 citations
TL;DR: On considere le probleme de diffusion dans un domaine ouvert Ω de R N ou N=2 ou 3, a frontiere C 2 connexe Γ et exterieur Ω e :=R N /Ω as mentioned in this paper
Abstract: On considere le probleme de diffusion dans un domaine ouvert Ω de R N ou N=2 ou 3, a frontiere C 2 connexe Γ et exterieur Ω e :=R N /Ω
132 citations
59 citations
TL;DR: In this paper, the authors consider the limit m→+∞ of solutions of the porous medium equation, where m = ∇•(um∇u)(xeRN), with N > 1, and conjecture that, for initial data with a unique maximum, the evolution is characterized by the onset of a "mesa" region, in which the solution is nearly spatially independent, surrounded by a region in which u is nearly equal to its initial value.
Abstract: In this paper we consider the limit m→+∞ of solutions of the porous-medium equation ut = ∇•(um∇u)(xeRN), with N > 1. We conjecture that, for initial data with a unique maximum, the evolution is characterized by the onset of a ‘mesa’ region, in which the solution is nearly spatially independent, surrounded by a region in which u is nearly equal to its initial value. The transition between these regions occurs near a surface which is identified with the free boundary in a certain Stefan problem which can be studied using variational inequalities. Moreover, singular-perturbation theory can be used to describe the structure of the transition region.
44 citations
40 citations
TL;DR: In this article, the singularites dans le prolongement analytique de la solution du problem de Dirichlet for l'equation de Helmholtz a 2 dimensions were studied.
Abstract: On etudie les singularites dans le prolongement analytique de la solution du probleme de Dirichlet pour l'equation de Helmholtz a 2 dimensions afin d'analyser les hypotheses de Rayleigh de la theorie de la diffusion
26 citations
23 citations
20 citations
TL;DR: In this article, the authors derived the zeroth and first order terms of the matched asymptotic expansion of the solutions, which are the sums of uniformly smooth outer terms (reduced solutions) and the exponentially varying inner terms (layer solutions).
Abstract: : In this paper the basic semiconductor device equations modelling a symmetric one-dimensional voltage-controlled diode are formulated as a singularly perturbed two point boundary value problem. The perturbation parameter is the normed Debye-length of the device. The authors derive the zeroth and first order terms of the matched asymptotic expansion of the solutions, which are the sums of uniformly smooth outer terms (reduced solutions) and the exponentially varying inner terms (layer solutions). The main result of the paper is that, if the perturbation parameter is sufficiently small then there exists a solution of the semiconductor device problem which is approximated uniformly by the zeroth order term of the expansion, even for large applied voltages. This result shows the validity of the asymptotic expansions of the solutions of the semiconductor device problem in physically relevant high-injection conditions.
18 citations
TL;DR: On peut montrer que plusieurs fonctions speciales importantes peuvent s'exprimer comme des derivees d'ordre complexe de Fonctions elementaires as mentioned in this paper.
Abstract: On peut montrer que plusieurs fonctions speciales importantes peuvent s'exprimer comme des derivees d'ordre complexe de fonctions elementaires
TL;DR: In this article, the authors utilise an approximation analytique for etudier les solutions periodiques and chaotiques de l'equation de Duffing forcee amortie.
Abstract: On utilise une approximation analytique pour etudier les solutions periodiques et chaotiques de l'equation de Duffing forcee amortie. Le forcage est de type fcoscot
TL;DR: In this article, the authors discuss un problem of type Stefan avec formation de vide, and propose a solution explicite, a solution which is explained in detail by the authors.
Abstract: On considere un probleme de type Stefan avec formation de vide. On donne une solution explicite
TL;DR: In this paper, a demonstration d'un theoreme donnant les conditions de l'existence d'une enveloppe de Lyapunov qui limite les solutions of a Lienard equation is presented.
Abstract: Demonstration d'un theoreme donnant les conditions de l'existence d'une enveloppe de Lyapunov qui limite les solutions d'une equation de type Lienard. Application d'un theoreme au mouvement de roulis d'un bateau
TL;DR: In this paper, the optimisation des methodes d'exploration du gaz and du petrole porte principalement sur les problemes de interpolation des donnees and sur l'estimation de reserves d'hydrocarbures recuperables mais non decouvertes.
Abstract: L'optimisation des methodes d'exploration du gaz et du petrole porte principalement sur les problemes d'interpolation des donnees et sur l'estimation de reserves d'hydrocarbures recuperables mais non decouvertes
TL;DR: In this paper, a theory de distribution stochasticique for le transport dans un milieu polyphasique a echelle multiple has been proposed, which is based on the concept of stochastique.
Abstract: On construit une theorie de distribution stochastique pour le transport dans un milieu polyphasique a echelle multiple
TL;DR: In this paper, a plaque is revetue par un revetement parfaitement absorbant sur sa face arrière, with respect to modification ouattenuation du champ sonore.
Abstract: La plaque est revetue par un revetement parfaitement absorbant sur sa face arriere. Effet de ce revetement sur la modification ou l'attenuation du champ sonore
TL;DR: In this article, a methode d'obtention de solutions approchees for des problemes d'ecoulement non visqueux is decrit for des problems d'hydrodynamique sous-marine and d'aerodynamique.
Abstract: On decrit une methode d'obtention de solutions approchees pour des problemes d'ecoulement non visqueux. Application a des problemes d'hydrodynamique sous-marine et d'aerodynamique
TL;DR: On considere la sedimentation axisymetrique d'une petite particule tournante et en translation dans un pore circulaire rempli de fluide qui communique avec un demi-espace de fluides as discussed by the authors.
Abstract: On considere la sedimentation axisymetrique d'une petite particule tournante et en translation dans un pore circulaire rempli de fluide qui communique avec un demi-espace de fluide
TL;DR: Ceci permet de formuler des inegalites variationnelles complementaires complementaires as mentioned in this paper, a formulation equivalente en utilisant la theorie des principes extremum duaux.
Abstract: Des problemes aux limites libres et mobiles peuvent se resoudre en utilisant la methode des inegalites variationnelles. On montre que l'on peut obtenir une formulation equivalente en utilisant la theorie des principes extremum duaux. Ceci permet de formuler des inegalites variationnelles complementaires
TL;DR: In this article, a decroissance exponentielle is used to combine a stationnaire and an ecoulement, which is caracterised by a decoissance exponentie.
Abstract: Etude dans l'approximation d'un gaz optiquement mince. Les temperatures des spheres sont elevees mais leur difference est faible de telle sorte que le nombre de Groshof est faible. L'ecoulement est caracterise par une decroissance exponentielle qui se superpose a un ecoulement stationnaire
TL;DR: Investigation theorique sur la detection and la mesure des defauts n'apparaissant pas a la surface des metaux par l'utilisation de champs de courant alternatif as mentioned in this paper.
Abstract: Investigation theorique sur la detection et la mesure des defauts n'apparaissant pas a la surface des metaux par l'utilisation de champs de courant alternatif