Co-volume methods for degenerate parabolic problems.
L.A. Baughman, N.J. Walkington (1993)
Numerische Mathematik
Meirmanov, A.M. (2007)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
Wei, Dongming, Zhang, Zhengbu (2001)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Adriano Montanaro (1994)
Rendiconti del Seminario Matematico della Università di Padova
Laurent Desvillettes, François Golse, Valeria Ricci (2014)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential equations governing the evolution of the temperature of each phase at a macroscopic level of description. The coupling terms describing the exchange of heat between the phases are obtained by using homogenization techniques originating from [D. Cioranescu, F. Murat,...
Michal Beneš (2003)
Applications of Mathematics
We investigate the motion by mean curvature in relative geometry by means of the modified Allen-Cahn equation, where the anisotropy is incorporated. We obtain the existence result for the solution as well as a result concerning the asymptotical behaviour with respect to the thickness parameter. By means of a numerical scheme, we can approximate the original law, as shown in several computational examples.
Nicolas Bouillard, Robert Eymard, Raphaele Herbin, Philippe Montarnal (2007)
ESAIM: Mathematical Modelling and Numerical Analysis
Modeling the kinetics of a precipitation dissolution reaction occurring in a porous medium where diffusion also takes place leads to a system of two parabolic equations and one ordinary differential equation coupled with a stiff reaction term. This system is discretized by a finite volume scheme which is suitable for the approximation of the discontinuous reaction term of unknown sign. Discrete solutions are shown to exist and converge towards a weak solution of the continuous problem. Uniqueness...
Petr Pauš, Michal Beneš (2009)
Kybernetika
This contribution deals with the numerical simulation of dislocation dynamics. Dislocations are described by means of the evolution of a family of closed or open smooth curves , . The curves are driven by the normal velocity which is the function of curvature and the position. The evolution law reads as: . The motion law is treated using direct approach numerically solved by two schemes, i. e., backward Euler semi-implicit and semi-discrete method of lines. Numerical stability is improved...
A. Bermúdez de Castro López (1979)
Collectanea Mathematica
Trudy Matematiceskogo Centra Imeni N. I. Lobacevskogo
G. M. Kremer, Ingo Müller (1997)
Annales de l'I.H.P. Physique théorique
Chumakov, G.A. (2007)
Sibirskij Matematicheskij Zhurnal
Mahmud, M.N., Idris, R., Hashim, I. (2009)
Differential Equations & Nonlinear Mechanics
Bhadauria, B.S., Debnath, Lokenath (2004)
International Journal of Mathematics and Mathematical Sciences
Mahmoud, Mostafa, Waheed, Shimaa (2010)
Mathematical Problems in Engineering
J. Kupka (1965)
Applicationes Mathematicae
Pavel Krejčí (2010)
Mathematica Bohemica
The paper deals with a model for water freezing in a deformable elastoplastic container. The mathematical problem consists of a system of one parabolic equation for temperature, one integrodifferential equation with a hysteresis operator for local volume increment, and one differential inclusion for the water content. The problem is shown to admit a unique global uniformly bounded weak solution.
Jiří Míčka, Oskar Schmidt (1957)
Aplikace matematiky
E. Magenes, R. H. Nochetto, C. Verdi (1987)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Alexander Kiselev, Leonid Ryzhik (2001)
Annales de l'I.H.P. Analyse non linéaire