Journal of Hebei University(Natural Science Edition) >

2019 , Vol. 39 >Issue 5: 449 - 454

DOI: https://doi.org/10.3969/j.issn.1000-1565.2019.05.001

Asymptotic properties for a porous media parabolic equations

  • XUE Yingzhen ,
  • FENG Heping
Expand
  • 1.School of Business, Xian International University, Xian 710077, China; 2.Intelligent Engineering Department, Hebei Software Institute, Baoding 071000, China

Received date: 2019-02-15

  Online published: 2019-09-25

Fold

Abstract

In order to describe the reaction diffusion problems of three media in physics, such as mechanics of porous media, fluid mechanics, gas flow and so on, the asymptotic behavior of a class of parabolic equations of porous media,with 3 variables coupled with a weighted nonlocal boundary and a nonlinear internal source is studied.The upper and lower solutions of the first eigenvalue are broken, and the upper and lower solutions of the equations are constructed by using the ordinary differential equation method, and the comparison theorem is quoted. It is proved that the whole existence of the solution of the parabolic equations of porous media with the power function and the exponential function fully coupled and the sufficient conditions for the solution in the finite time blasting are obtained.On the basis of the existing results, provide more theoretical support for porous media and fluid mechanics are achieved.

Key words： porous media parabolic equations; the comparison principle; global solution; blow up

Cite this article

XUE Yingzhen , FENG Heping . Asymptotic properties for a porous media parabolic equations[J]. Journal of Hebei University(Natural Science Edition), 2019 , 39(5) : 449 -454 . DOI: 10.3969/j.issn.1000-1565.2019.05.001

References

[1] 杨婕,刘丙辰,张长城.具有非局部边界的退化抛物方程组的爆破解[J].数学杂志,2017,37(6): 1275-1286.DOI:10.13548/j.sxzz.20161108.002.
[2] 钟光胜,田立新.具有非线性范数型源的反应扩散方程组解的爆破性质[J].数学杂志,2017(1):129-137.DOI:10.13548/j.sxzz.20160322.002.
[3] LIU BC, ZHANG CC. Critical exponents in porous media equations with weighted nonlocal boundary conditions[J]. Journal of Mathematics,2015,35(1):51-62.DOI:10.13548/j.sxzz.2015.01.006.
[4] 王文海.具非局部源和非局部边界条件抛物方程组解的性质[J].中北大学学报(自然科学版), 2012, 33(4): 372-375.DOI:10.3969/j.issn.1673-3193.2012.04.005.
[5] MU C L, SU Y. Global existence and blow up for a quasilinear degenerateparabolic system in a ylinder[J]. Appi Math Letters,2001,14(1):715-723. DOI:10.1016/S0893-9659(01)80032-X.
[6] PAO C V.Nonlinear parabolic and elliptic equations[M].London:Plenum Press,1992.
[7] WANG S,WANG M X,XIE C H.A nonlinear degenerate diffusion equation not in divergence form[J].Zeitschrift Für Angewandte Mathematik Und Physik Zamp,2000,51(1): 149-159.DOI:10.1007/PL00001503.
[8] LI Y X,DENG W B,XIE C H.Global existence and nonexistence for degenerate parabolic systems[J].Nonlinear Analysis,2002,55(3):233-244.DOI:10.1090/S0002-9939-02-06630-3.
[9] DENG W B,LI Y X,XIE C H.Existence and nonexistence of global solution of some nonlocal degenerate parabolic system[J].Proceedings of the American Mathematical Society,2003,131(5):1573-1582.DOI: 10.1016 /s0893-9659( 03)80118-0.
[10] ZHANG Y,SONG X J.Global existence and blow-up for a degenerate parabolic systems with nonlocal source [J].Journal of Southwest University(Natural Science Edition),2008,30(9):80-84.DOI:10.13718/j.cnki.xdzk.2008.09.013.
[11] BUDDAL C J,DOLD J W,GALAKTIONOV V A.Global blow-up for a semilinear heat equation on a subspace[J].Proceedings of the Royal Society of Edinburgh:Section A Mathematics,2015(5):893-923. DOI: 10.1017 /s0308210515000256.
[12] ZHANG H,KONG L H,ZHENG S N. Propagations of singularities in a parabolic system with coupling nonlocal sources[J].Sci in China: Ser A,2009,52(1):181-194.DOI:10.3969 /j.issn.1006-8341.2009. 02.009.
[13] 叶其孝,李正元,王明新,等.反应扩散方程引论[M] 第2版.北京:科学出版社,2011.
Options
Outlines

/

〈 〉