DOUBLY NONLINEAR PARABOLIC EQUATIONS INVOLVING p-LAPLACIAN OPERATORS VIA TIME-DISCRETIZATION METHOD

Title & Authors
DOUBLY NONLINEAR PARABOLIC EQUATIONS INVOLVING p-LAPLACIAN OPERATORS VIA TIME-DISCRETIZATION METHOD
Shin, Kiyeon; Kang, Sujin;

Abstract
In this paper, we consider a doubly nonlinear parabolic partial differential equation $\frac{{\partial}{\beta}(u)}{{\partial}t}-{\Delta}_pu+f(x,t,u) Keywords doubly nonlinear;p-Laplacian;Rothe method; Language English Cited by References 1. R. Adams, Sobolev Spaces, Academic Press, New York, 1975. 2. V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noord-hoff Internat. Publ., Leyden, 1976. 3. A. Bensoussan, L. Boccardo, and F. Murat, On a nonlinear partial differential equation having natural growth terms and unbounded solution, Ann. Inst. H. Poincare Anal. Non Lineaire 5 (1988), no. 4, 347-364. 4. J. I. Diaz and J. F. Padial, Uniqueness and existence of solutions in the BVt(Q) space to a doubly nonlinear parabolic problem, Differential Integral Equations 40 (1996), no. 2, 527-560. 5. A. Eden, B. Michaux, and J. M. Rakotoson, Semi-discretized nonlinear evolution equa- tions as discrete dynamical systems and error analysis, Indiana Univ. Math. J. 39 (1990), no. 3, 737-783. 6. A. Eden, B. Michaux, and J. M. Rakotoson, Doubly nonlinear parabolic type equations as dynamical systems, J. Dynam. Differential Equations 3 (1991), no. 1, 87-131. 7. M. Efendiev and A. Miranville, New models of Cahn-Hilliard-Gurtin equations, Contin. Mech. Thermodyn. 16 (2004), no. 5, 441-451. 8. A. El Hachimi and H. El Ouardi, Existence and regularity of a global attractor for doubly nonlinear parabolic equations, Electron. J. Differential Equations 2002 (2002), no. 45, 1-15. 9. M. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Phys. D. 92 (1996), no. 3-4, 178-192. 10. A. G. Kartasatos and M. E. Parrott, The weak solution of a functional-differential equation in a general Banach space, J. Differential Equations 75 (1988), no. 2, 290-302. 11. V. Le and K. Schmit, Global Bifurcation in Variational Inequalities, Springer-Verlag, New York, 1997. 12. N. Merazga and A. Bouziani, On a time-discretization method for a semilinear heat equation with purely integral conditions in a nonclassical function space, Nonlinear Analysis 66 (2007), no. 3, 604-623. 13. A. Miranville and G. Schimperna, Global solution to a phase transition model based on a microforce balance, J. Evol. Equ. 5 (2005), no. 2, 253-276. 14. F. Otto,$L^1\$-contraction and uniqueness for quasilinear elliptic-parabolic equations, J. Differential Equations 131 (1996), no. 1, 20-38.

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