Approximation de certaines équations paraboliques non linéaires. (French) Zbl 0336.35058


35K55 Nonlinear parabolic equations
35A35 Theoretical approximation in context of PDEs
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
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[1] H. Brezis, M. Sibony,Méthodes d’approximation et d’itération pour les opérateurs monotones, Arch. Rat. Mech. Anal.28 (1968), 59–82. · Zbl 0157.22501 · doi:10.1007/BF00281564
[2] M. Crouzeix,Sur l’approximation des equations differentielles operationnelles linéaires par des méthodes de Runge-Kutta, Thèse, Parigi 1975.
[3] J. Douglas,A note on the alternating direction implicit method for the numerical solution of heat flow problems, Proc. Am. Math. Soc.,8 (1957), 409–411. · Zbl 0077.11304 · doi:10.1090/S0002-9939-1957-0090876-7
[4] J. Douglas–T. Dupont,Galerkin methods for parabolic equations, SIAM J. Num. Anal.7 (1970), 575–626. · Zbl 0224.35048 · doi:10.1137/0707048
[5] G. Geymonat,Quelques remarques sur l’utilisation des méthodes itératives dans l’approximation des solutions des équations paraboliques linéaires, Inst. Nazionale di Alta Mat., Symposia Math.,10 (1972), 381–402.
[6] J. L. Lions,Quelques méthodes de résolution des problèmes aux limites non linéaires (1969), Dunod, Gauthier-Villars.
[7] J. L. Lions–E. Magenes,Problèmes aux limites non homogènes et applications (1968), Dunod, Gauthier-Villars.
[8] W. V. Petryshin,On the extension and the solution of non linear operator equations, Illinois Journal of Math.,10, (1966), 255–274.
[9] M. Sibony,Sur l’approximation d’équations et inéquations aux dérivées partielles non linéaires de type monotone, Journal of Math. Analysis and Appl.,34, (1971), 502–564. · Zbl 0216.42201 · doi:10.1016/0022-247X(71)90095-3
[10] R. Temam,Sur la stabilité et la convergence de la méthode des pas fractionnaires, Annali di Mat. Pura ed Appl. LXXIX (1968), 191–380. · Zbl 0174.45804 · doi:10.1007/BF02415183
[11] E. L. Washspress,Iterative solution of elliptic systems (1966), Prentice Hall.
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