Advanced Search
Article Contents
Article Contents

Global existence and blow-up of solutions to a singular Non-Newton polytropic filtration equation with critical and supercritical initial energy

  • * Corresponding author

    * Corresponding author
This work is partially supported by the the Basic and Advanced Research Project of CQC-STC grant cstc2016jcyjA0018 and NSFC 11201380.
Abstract Full Text(HTML) Related Papers Cited by
  • In this paper, we revisit the singular Non-Newton polytropic filtration equation, which was studied extensively in the recent years. However, all the studies are mostly concerned with subcritical initial energy, i.e., $E(u_0)<d$ , where $E(u_0)$ is the initial energy and $d$ is the mountain-pass level. The main purpose of this paper is to study the behaviors of the solution with $E(u_0)≥d$ by potential well method and some differential inequality techniques.

    Mathematics Subject Classification: 35B33, 35K50, 35K55, 35K63.


    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] M. Badiale and G. Tarantello, A sobolev-hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics, Archive for Rational Mechanics and Analysis, 163 (2002), 259-293. 
    [2] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer New York, 2010.
    [3] F. Gazzola and T. Weth, Finite time blow-up and global solutions for semilinear parabolic equations with initial data at high energy level, Differential and Integral Equations, 18 (2005), 961-990. 
    [4] B. Guo and W. J. Gao, Blow-up of solutions to quasilinear hyperbolic equations with $p(x,t)$-laplacian and positive initial energy, Comptes Rendus Mecanique, 342 (2014), 513-519. 
    [5] A. J. Hao and J. Zhou, A new blow-up condition for semi-linear edge degenerate parabolic equation with singular potentials, Applicable Analysis, (2016), 1-12. 
    [6] Y. HuJ. Li and L. W. Wang, Blow-up phenomena for porous medium equation with nonlinear flux on the boundary, Journal of Applied Mathematics, 2013 (2013), 1-5. 
    [7] A. Khelghati and K. Baghaei, Blow-up phenomena for a nonlocal semilinear parabolic equation with positive initial energy, Computers and Mathematics with Applications, 70 (2015), 896-902. 
    [8] Q. W. LiW. J. Gao and Y. Z. Han, Global existence blow up and extinction for a class of thin-film equation, Nonlinear Analysis Theory Methods and Applications, 147 (2016), 96-109. 
    [9] L. R. Luo and J. Zhou, Global existence and blow-up to the solutions of a singular porous medium equation with critical initial energy, Boundary Value Problems, 2016 (2016), 1-8. 
    [10] X. L. WuB. Guo and W. J. Gao, Blow-up of solutions for a semilinear parabolic equation involving variable source and positive initial energy, Applied Mathematics Letters, 26 (2013), 539-543. 
    [11] X. L. Wu and W. J. Guo, Blow-up of the solution for a class of porous medium equation with positive initial energy, Acta Math Sci, 33 (2013), 1024-1030. 
    [12] Z. Q. Wu, J. X. Yin, H. L. Li and J. N. Zhao, Nonlinear diffusion equations. World Scientific Publishing Co. inc. river Edge Nj, 2001.
    [13] R. Z. Xu and J. Su, Global existence and finite time blow-up for a class of semilinear pseudo-parabolic equations, Journal of Functional Analysis, 264 (2013), 2732-2763. 
    [14] Y. Wang, The existence of global solution and the blowup problem for some $p$-laplace heat equations, Acta Math Sci, 27 (2007), 274-282. 
    [15] Z. Tan, Non-Newton Filtration Equation with special medium void, Acta Math Sci, 24B (2014), 118-128. 
    [16] J. Zhou, A multi-dimension blow-up problem to a porous medium diffusion equation with special medium void, Applied Mathematics Letters, 30 (2014), 6-11. 
    [17] J. Zhou, Global existence and blow-up of solutions for a non-newton polytropic filtration system with special volumetric moisture content, Computers and Mathematics with Applications, 71 (2016), 1163-1172. 
  • 加载中

Article Metrics

HTML views(390) PDF downloads(348) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint