[ APERÇU GENERAL SUR LES EQUATIONS AUX DERIVEES PARTIELLES NON LINEAIRES ]
Volume 18, Issue 1, October 2016, Pages 166–190
Théodore Mapendo Wendo1
1 Département de Mathématique-physique, Institut Supérieur Pédagogique d’Idjwi (ISP-IDJWI), Idjwi, Sud-Kivu, RD Congo
Original language: French
Copyright © 2016 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The mathematical notion of nonlinear partial derivatives equations are registered in full in Mathematical Analysis. This concept has several applications in other disciplines such as physics, economics, demography, chemistry, differential geometry and infinitesimal, etc. Presented with diversified forms, this notion remains essential in the progress of all research in pure and applied mathematics. It borrows concepts of topology and functional analysis for a better understanding. The question is at what level mathematics are for research and our contribution in this article. For this, we present the theory and develop some methods of solving equations to nonlinear partial differential equations.
Author Keywords: metric space, topological space, normed vector space, space of SOBOLEV, equation of KORTEWEG and VRIES, REACTION-RELEASE equation, Navier-Stokes equation.
Volume 18, Issue 1, October 2016, Pages 166–190
Théodore Mapendo Wendo1
1 Département de Mathématique-physique, Institut Supérieur Pédagogique d’Idjwi (ISP-IDJWI), Idjwi, Sud-Kivu, RD Congo
Original language: French
Copyright © 2016 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The mathematical notion of nonlinear partial derivatives equations are registered in full in Mathematical Analysis. This concept has several applications in other disciplines such as physics, economics, demography, chemistry, differential geometry and infinitesimal, etc. Presented with diversified forms, this notion remains essential in the progress of all research in pure and applied mathematics. It borrows concepts of topology and functional analysis for a better understanding. The question is at what level mathematics are for research and our contribution in this article. For this, we present the theory and develop some methods of solving equations to nonlinear partial differential equations.
Author Keywords: metric space, topological space, normed vector space, space of SOBOLEV, equation of KORTEWEG and VRIES, REACTION-RELEASE equation, Navier-Stokes equation.
Abstract: (french)
La notion mathématique d’équations aux dérivées partielles non linéaires s’inscrit en intégralité en Analyse mathématique. Cette notion trouve plusieurs applications dans d’autres disciplines comme la physique, l’économie, la démographie, la chimie, la géométrie différentielle et infinitésimale, etc. Présentée avec des formes diversifiées, cette notion reste incontournable dans le progrès de toute recherche en mathématique pure ou appliquée. Elle emprunte des notions de topologie et d’analyse fonctionnelle pour une meilleure compréhension. La question est de savoir à quel niveau les matheux en sont pour la recherche et notre apport dans le présent article. Pour cela, nous présentons la théorie et développons quelques méthodes de résolution des équations aux dérivées partielles non linéaires.
Author Keywords: Espace métrique, espace topologique, espace vectoriel normé, espace de SOBOLEV, équation de KORTEWEG et de VRIES, équation de REACTION-DIFFUSION, équation de NAVIER-STOKES.
How to Cite this Article
Théodore Mapendo Wendo, “OVERVIEW ON NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS,” International Journal of Innovation and Applied Studies, vol. 18, no. 1, pp. 166–190, October 2016.
