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http://dx.doi.org/10.7858/eamj.2010.26.3.403

DOUBLY NONLINEAR PARABOLIC EQUATIONS RELATED TO THE LERAY-LIONS OPERATORS: TIME-DISCRETIZATION  

Shin, Ki-Yeon (DEPARTMENT OF MATHEMATICS PUSAN NATIONAL UNIVERSITY)
Kang, Su-Jin (DEPARTMENT OF MATHEMATICS PUSAN NATIONAL UNIVERSITY)
Publication Information
East Asian mathematical journal / v.26, no.3, 2010 , pp. 403-413 More about this Journal
Abstract
In this paper, we consider a doubly nonlinear parabolic equation related to the Leray-Lions operator with Dirichlet boundary condition and initial data given. By exploiting a suitable implicit time-discretization technique, we obtain the existence of global strong solution.
Keywords
doubly nonlinear; Leray-Lions operator; time-discretization;
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1 J. M. Rakotoson, On some degenerate and nondegenerate Quasilinear Elliptic systems with nonhomogeneous Dirichlet boundary condition, Nonl. Anal. T.M.A. 13 (1989), no. 2, 165-183.   DOI   ScienceOn
2 V. Le and K. Schmit, Global Bifurcation in Variational Inequalities, Springer-Verlag, New York. Inc. 1997.
3 A. Miranville and G. Schimperna, Global solution to a phase transition model based on microforce balance, J. evol. equ. 5 (2005), 253-276.   DOI   ScienceOn
4 A. Rougirel, Convergence to steady state and attractors for doubly nonlinear equations, J. Math. Anal. Appl. 339 (2008), 281-294.   DOI   ScienceOn
5 M. Schatzman, Stationary solutions and asymptotic behavior of a Quasilinear degener- ate parabolic equation, Indiana Univ. Math. J. 33 (1984), no. 1, 1-29.   DOI
6 R. E. Showalter, Monotone operators in Banach space and nonlinear partial dierential equations, Math. Surveys and Monographs 49, Amer. Math. Soc., 1996.
7 R. Adams, Sovolev Spaces, Academic Press, New York, 1975.
8 V. Barbu, Nonlinear semigroups and dierential equations in Banach spaces, Noordho Internat. Publ., Leyden, 1976.
9 A. Bensoussan, L. Boccardo and F. Murat, On a nonlinear P.D.E. having natural growth terms and unbounded solutions, Ann. Inst. H. Poincare. 5 (1988), no. 4, 347-364.
10 A. Eden, B. Michaux and J. M. Rakotoson, Semidiscretized nonlinear evolution equa- tions as discrete dynamical systems and error analysis, Indiana University Mathematics J. 39 (1990), no. 3, 737-783   DOI
11 A. Eden, B. Michaux and J. M. Rakotoson, Doubly nonlinear parabolic type equations as dynamical systems, J. Dynam. Di. Equ. 3 (1991), no. 1, 87-131.   DOI
12 A. El Hachimi and H. El. Ouardi, Existence and regularity of a global attractor for doubly nonlinear parabolic equations, Electronic J. Di. Equ. 2002 (2002), no. 45, 1-15.
13 M. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a mi- croforce balance, Phys.D 92 (1996), 178-192.   DOI   ScienceOn