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Topological Methods in Nonlinear Analysis

The long-time behavior of weighted p-Laplacian equations
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The long-time behavior of weighted p-Laplacian equations

Authors

  • Shan Ma
  • Hongtao Li

Keywords

Global existence of solutions, global attractors, weighted $p$-Laplacian equations

Abstract

In this work we study weighted $p$-Laplacian equations in abounded domain with a variable and generally non-smooth diffusion coefficient having at most a finite number of zeroes. The main attention is focused on the case that the diffusion coefficient $a(x)$ in such equations satisfies the inequality $\liminf\limits_{x\to z}|x-z|^{-p}a(x)> 0$ for every $ z\in \overline\Omega$. We show the existence of weak solutions and global attractors in $L^2(\Omega)$, $L^q(\Omega)(q\geq 2)$ and $D_0^{1,p}(\Omega)$, respectively.

References

C.T. Anh, N.M. Chuong and T.D. Ke, global attractors for the m-semiflow generated by a quasilinear degenerate parabolic equations, J. Math. Anal. Appl. 363 (2010), 444–453.

C.T. Anh and P.Q. Hung, global attractors for a class of degenerate parabolic equations, Acta Math. Vietnam. 34 (2009), 213–231.

C.T. Anh and T.D. Ke, Long-time behavior for quasilinear parabolic equations involving weighted p-Laplacian operators, Nonlinear Anal. 71 (2009), 4415–4422.

A.V. Babin and M.I. Vishik, Attractors of Evolution Equations, North-Holland, Amsterdam, 1992.

P. Caldiroli and R. Musina, On a variational degenerate elliptic problem, Nonlinear Differential Equations Appl. 7 (2000), 187–199.

J.W. Cholewa and T. Dlotko, Global Attractors in Abstract Parabolic Problems, Cambridge University Press, Cambridge, 2000.

R. Dautray and J.L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. I. Physical Origins and Classical Methods, Springer–Verlag, Berlin, 1985.

E. Dibenedetto, Degenerate Parabolic Equations, Springer–Verlag, NewYork, 1993.

N.I. Karachalios and N.B. Zographopoulos, Convergence towards attractors for a degenerate Ginzburg–Landau equation, Z. Angew. Math. Phys. 56 (2005), 11–30.

N.I. Karachalios and N.B. Zographopoulos, On the dynamics of a degenerate parabolic equation global bifurcation of stationary states and convergence, Calc. Var. 25 (2006), no. 3, 361–393.

N.I. Karachalios and N.B. Zographopoulos, Global attractors and convergence to equilibrium for degenerate Ginzburg–Landau and parabolic equations, Nonlinear Anal. 63 (2005), e1749–e1768.

A.Kh. Khanmamedov, Global attractors for one dimensional p-Laplacian equation, Nonlinear Anal. 71 (2009), no. 1–2, 155–171.

H. Li and S. Ma, Asymptotic behavior of a class of degenerate parabolic equations, Abstr. Appl. Anal. (2012), Art. ID 673605, 15 pp.

H. Li, S. Ma and C. Zhong, Long-time behavior for a class of degenerate parabolic equations, Discrete Contin. Dyn. Syst. 34 (2014), no. 7, 2873–2892.

Q.F. Ma, S.H. Wang and C.K. Zhong, Necessary and sufficient conditions for the existence of global attractors for semigroups and applications, Indiana University Math. J. 51 (2002), no. 6, 1541–1557.

I. Peral, Multiplicity of Solutions for the p-Laplacian, International Center for Theoretial Phusics Trieste, 1997.

J.C. Robinson, Infinite-Dimensional Dynamical Systems. An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors, Cambridge University Press, 2001.

R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, 2nd edition, Berlin, Springer, 1997.

M. Yang, Ch. Sun and Ch.Zhong, Existenceof a global attractor for a p-Laplacian equation in RN , Nonlinear Anal. 66 (2007), 1–13.

J.X. Yin and C.P. Wang, Evolutionary weighted p-laplacian equation, J. Differential Equations 237 (2007), 421–445.

C.K. Zhong, M.H. Yang and C.Y. Sun, The existence of global attractors for the normto-weak continuous semigroup and its application to the nonlinear reaction-diffusion equations, J. Differential Equations 223 (2006), 367–399.

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Published

2019-07-27

How to Cite

1.
MA, Shan and LI, Hongtao. The long-time behavior of weighted p-Laplacian equations. Topological Methods in Nonlinear Analysis. Online. 27 July 2019. Vol. 54, no. 2, pp. 685 - 700. [Accessed 6 July 2025].
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