Exponential time decay of solutions to a nonlinear fourth-order parabolic equation

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 54, Issue 3, 2003, Pages 377-386

  Jungel A ^a   Toscani, G ^b  

^a UNIVERSITY OF KONSTANZ   (Germany)

^b UNIVERSITY OF PAVIA   (Italy)

Author keywords

Asymptotic behavior; Diffusion equation; Entropy dissipation; Higher order parabolic equation

Indexed keywords

EID: 0038407258     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-003-1026-y     Document Type: Article

References (11)

1. A. Arnold, P. Markowich, G. Toscani, and A. Unterreiter, On logarithmic Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations. Comm. P.D.E. 26 (2001), 43-100.
2. A. Arnold, P. Markowich, G. Toscani, and A. Unterreiter, On generalized Csisźar-Kullback inequalities, Monatshefte für Mathematik 131 (2000), 235-53.
3. P. Bleher, J. Lebowitz, and E. Speer, Existence and positivity of solutions of a forth-order nonlinear PDE describing interface fluctuations, Comm. Pure Appl. Math. 47 (1994), 923-942.
4. J.A. Carrillo, A. Jüngel, P. Markowich, G. Toscani, and A. Unterreiter, Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities, Monatshefte für Mathematik 133 (2001), 1-82.
5. A. L. Bertozzi and M. Pugh, The lubrication approximation for thin viscous films: regularity and long-time behavior of weak solutions, Comm. Pure Appl. Math. 49 (1996), 85-123.
6. 1 -decay of solutions of the porous media equation to self-similarity, Indiana Univ. Math. J. 49 (2000), 113-141.
7. J.A. Carrillo and G. Toscani, Long-time asymptotics for strong solutions of the thin film equation, Comm. Math. Phys. 225 (2002), 551-571.
8. A. Jüngel and R. Pinnau, Global non-negative solutions of a fourth-order nonlinear parabolic equation for quantum systems, SIAM J. Math. Anal. 32 (2000), 760-777.
9. A. Jüngel and R. Pinnau, A positivity-preserving numerical scheme for a fourth-order parabolic equation, SIAM J. Num. Anal. 39 (2001), 385-406
10. J. L. Lopez, J. Soler, and G. Toscani, Time rescaling and asymptotic behavior of some fourth order degenerate diffusion equations, Comput. Math. Appl. 43 (2002), 721-736.
11. T. G. Myers, Thin films with high surface tension, SIAM Reviews 40 (1998), 441-462.