Browse > Article
http://dx.doi.org/10.14317/jami.2014.547

SOME PROPERTIES OF SOLUTIONS FOR A SIXTH-ORDER PARABOLIC EQUATION IN ONE SPATIAL DIMENSION  

Zhao, Xiaopeng (School of Science, Jiangnan University)
Publication Information
Journal of applied mathematics & informatics / v.32, no.3_4, 2014 , pp. 547-554 More about this Journal
Abstract
In this paper, we consider the existence and uniqueness of global weak solution for a sixth-order classical surface-diffusion equation in one spatial dimension. Moreover, the regularity and blow-up of solutions are also studied.
Keywords
Sixth-order diffusion equation; existence; regularity; blow-up;
Citations & Related Records
연도 인용수 순위
  • Reference
1 J. Yin, On the Cahn-Hilliard equation with nonlinear principal part, J. Partial Differential Equations, 7(1994), 77-96.
2 A. A. Golovin, M. S. Levine, T. V. Savina, S. H. Davis, Faceting instability in the presernce of wetting interactions: A mechanism for the formation of quantum dots, Phys. Rev. B, 70(2004), 235342.   DOI   ScienceOn
3 A. Jungel, J. Milisic, A sixth-order nonlinear parabolic equation for quantum systems, SIAM J. Math. Anal., 41(4)(2009), 1472C1490.   DOI   ScienceOn
4 C. Liu, Regularity of solutions for a sixth order nonlinear parabolic equation in two space dimensions, Annales Polonici Mathematici, In press.
5 O. A. Ladyzhenskaja, V. A. Solonikov, N. N.Ural'ceva, Linear and Quasilinear Equations of Parabolic Type. Amer. Math. Soc., Providence, RI, 1968.