Abstract
We deal with the existence of weak solutions of double degenerate quasilinear parabolic inequalities with a Signorini-Dirichlet-Neumann type mixed boundary condition, which may degenerate in certain subset of the boundary or on a segment in the interior of the domain and in time. The main tools in our study are the maximal monotone property of the derivative operator with zero-initial valued conditions and the theory of pseudomonotone perturbations of maximal monotone mappings.
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References
Browder, F. Nonlinear operators and nonlinear equations of evolution in Banach spaces. In: Proceedings of symposia in pure mathematics; Vol. 18, pt.2 American Mathematical Society, Providence, Rhode Island, 1976
Drabek, P., Kufner, A., Nicolosi, F. On the solvability of degenerated quasilinear elliptic equations of higher order. J. Differential Equations, 109: 325–347 (1994)
Gan, X.Q. Existence of weak solutions for double degenerated parabolic equations with measures as data. Chinese Science Bulletin, 40(15): 1354–1356 (1995)
Liu, Z.H. Nonlinear degenerate parabolic equations. Acta Math. Hungar., 77: 147–157 (1997)
Liu, Z.H. A class of evolution hemivariational inequalities. Nonlinear Analysis, TMA., 36(1): 91–100 (1999)
Liu, Z.H. Periodic solutions for double degenerate quasilinear parabolic equations. Nonlinear Analysis, TMA., 51(7): 1245–1257 (2002)
Liu, Z.H. On Doubly Degenerate Quasilinear Parabolic Equations of Higher Order. Acta Mathematica Sinica, English Series, 21(1): 197–208 (2005)
Liu, Z.H. Existence results for quasilinear parabolic hemivariational inequalities. J. Differential Equations, 244: 1395–1409 (2008)
Liu, Z.H. Anti-periodic solutions to nonlinear evolution equations. Journal of Functional Analysis, 258(6): 2026–2033 (2010)
Yin, J.X., Gao, W.J. Flows through nonhomogeneous porous media in an isolated environment. Quart. Appl. Math., 55(2): 333–346 (1997)
Zeidler, E. Nonlinear Functional Analysis and Its Applications, IIA and IIB. Springer-Verlag, New York, 1990
Zhao, J.N. Stability of solutions for a class of quasilinear degenerate parabolic equations. Northeast Math. J., 10(2): 279–284 (1994)
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Project Supported by the National Natural Science Foundation of China (Grant No.11271087, No.61263006) and Guangxi Scientific Experimental (China-ASEAN Research) Centre No.20120116.
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Liu, Gf., Liu, Yl. On double degenerate quasilinear parabolic variational inequalities. Acta Math. Appl. Sin. Engl. Ser. 29, 861–868 (2013). https://doi.org/10.1007/s10255-013-0263-x
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DOI: https://doi.org/10.1007/s10255-013-0263-x