K. Azelmat, M. Kbiri Alaoui, D. Meskine, A. Souissi, "Parabolic inequalities in as limits of renormalized equations", International Journal of Mathematics and Mathematical Sciences, vol. 2006, Article ID 046265, 18 pages, 2006. https://doi.org/10.1155/IJMMS/2006/46265
Parabolic inequalities in as limits of renormalized equations
The paper deals with the existence of solutions of some parabolic bilateral problems approximated by the renormalized solutions of some parabolic equations.
- L. Boccardo, F. Murat, and J.-P. Puel, “Existence of bounded solutions for nonlinear elliptic unilateral problems,” Annali di Matematica Pura ed Applicata, vol. 152, no. 1, pp. 183–196, 1988.
- F. Donati, “A penalty method approach to strong solutions of some nonlinear parabolic unilateral problems,” Nonlinear Analysis, vol. 6, no. 6, pp. 585–597, 1982.
- R. Landes, “On the existence of weak solutions for quasilinear parabolic initial-boundary value problems,” Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, vol. 89, no. 3-4, pp. 217–237, 1981.
- R. Landes and V. Mustonen, “A strongly nonlinear parabolic initial-boundary value problem,” Arkiv för Matematik, vol. 25, no. 1, pp. 29–40, 1987.
- J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris; Gauthier-Villars, Paris, 1969.
- D. Meskine and A. Elmahi, “On the limit of some nonlinear parabolic problems,” Archives of Inequalities and Applications, vol. 2, no. 4, pp. 499–515, 2004.
- M. C. Palmeri, “Homographic approximation for some nonlinear parabolic unilateral problems,” Journal of Convex Analysis, vol. 7, no. 2, pp. 353–373, 2000.
- A. Porretta, “Existence results for nonlinear parabolic equations via strong convergence of truncations,” Annali di Matematica Pura ed Applicata, vol. 177, pp. 143–172, 1999.
- M. Rudd, Nonlinear constrained evolution in Banach spaces, M.S. thesis, University of Utah, Utah, 2003.
- M. Rudd, “Weak and strong solvability of parabolic variational inequalities in Banach spaces,” Journal of Evolution Equations, vol. 4, no. 4, pp. 497–517, 2004.
- J. Simon, “Compact sets in the space ,” Annali di Matematica Pura ed Applicata, vol. 146, no. 1, pp. 65–96, 1987.
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