CRITICAL EXTINCTION EXPONENTS FOR POLYTROPIC FILTRATION EQUATIONS WITH NONLOCAL SOURCE AND ABSORPTION

doi:10.1016/S0252-9602(15)60008-X

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (2): 366-374.doi: 10.1016/S0252-9602(15)60008-X

CRITICAL EXTINCTION EXPONENTS FOR POLYTROPIC FILTRATION EQUATIONS WITH NONLOCAL SOURCE AND ABSORPTION

李海霞, 韩玉柱, 高文杰

School of Mathematics, Jilin University, Changchun 130012, China

收稿日期:2013-10-09 修回日期:2014-01-01 出版日期:2015-03-20 发布日期:2015-03-20
基金资助:
This project is supported by NSFC (11271154, 11401252), Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education, the 985 program of Jilin University, and Fundamental Research Funds of Jilin University (450060501179). The first author is also supported by Graduate Innovation Fund of Jilin University (2014084).

CRITICAL EXTINCTION EXPONENTS FOR POLYTROPIC FILTRATION EQUATIONS WITH NONLOCAL SOURCE AND ABSORPTION

Haixia LI, Yuzhu HAN, Wenjie GAO

School of Mathematics, Jilin University, Changchun 130012, China

Received:2013-10-09 Revised:2014-01-01 Online:2015-03-20 Published:2015-03-20
Supported by:
This project is supported by NSFC (11271154, 11401252), Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education, the 985 program of Jilin University, and Fundamental Research Funds of Jilin University (450060501179). The first author is also supported by Graduate Innovation Fund of Jilin University (2014084).

摘要/Abstract

摘要：

In this article, by applying the super-solution and sub-solution methods, instead of energy estimate methods, the authors investigate the critical extinction exponents for a polytropic filtration equation with a nonlocal source and an absorption term, and give a classification of the exponents and coefficients for the solutions to vanish in finite time or not, which improve one of our results (Applicable Analysis, 92(2013), 636-650) and the results of Zheng et al (Math. Meth. Appl. Sci., 36(2013), 730-743).

关键词: Polytropic filtration equation, critical exponent, extinction, super-solution and sub-solution

Abstract:

Key words: Polytropic filtration equation, critical exponent, extinction, super-solution and sub-solution

中图分类号:

35K55

李海霞, 韩玉柱, 高文杰. CRITICAL EXTINCTION EXPONENTS FOR POLYTROPIC FILTRATION EQUATIONS WITH NONLOCAL SOURCE AND ABSORPTION[J]. 数学物理学报(英文版), 2015, 35(2): 366-374.

Haixia LI, Yuzhu HAN, Wenjie GAO. CRITICAL EXTINCTION EXPONENTS FOR POLYTROPIC FILTRATION EQUATIONS WITH NONLOCAL SOURCE AND ABSORPTION[J]. Acta mathematica scientia,Series B, 2015, 35(2): 366-374.

参考文献

[1] Dibenedetto E. Degenerate Parabolic Equations. Berlin: Springer-Verlag, 1993

[2] Vázquez J L. The porousmedium equation, Mathematical Theory. Oxford Mathematical Monographs. Ox- ford: Oxford University Press, 2007

[3] Calsina A, Perello C, Saldana J. Non-local reaction-diffusion equations modelling predator-prey coevolution. Publ Math, 1994, 32: 315-325

[4] Furter J, Grinfeld M. Local vs nonlocal interactions in population dynamics. J Math Biol, 1989, 27: 65-80

[5] Galaktionov V A, Peletier L A, Vazquez J L. Asymptotics of fast-diffusion equation with critical exponent. SIAM J Math Anal, 2000, 31: 1157-1174

[6] Galaktionov V A, Vazquez J L. Asymptotic behavior of nonlinear parabolic equations with critical expo- nents. A dynamical system approach. J Funct Anal, 1991, 100: 435-462

[7] Galaktionov V A, Vazquez J L. Extinction for a quasilinear heat equation with absorption I. Technique of intersection comparison. Commun Partial Differential Equations, 1994, 19: 1075-1106

[8] Galaktionov V A, Vazquez J L. Extinction for a quasilinear heat equation with absorption II. A dynamical system approach. Commun Partial Differential Equations, 1994, 19: 1107-1137

[9] Han Y Z, Gao W J. Extinction for a fast diffusion equation with a nonlinear nonlocal source. Arch Math, 2011, 97: 353-363

[10] Han Y Z, Gao W J. Extinction and non-extinction for a polytropic filtration equation with a nonlocal source. Appl Anal, 2013, 92: 636-650

[11] Leoni G. A very singular solution for the porous media equation u_t = Δu^m - u^p when 0
[12] Liu W J, Wang M X, Wu B. Extinction and Decay Estimates of Solutions for a Class of Porous Medium Equations. J Inequalities and Applications, 2007, 2007: 1-8

[13] Wang Y F, Yin J X. Critical extinction exponents for a polytropic filtration equation with absorption and source. Math Method Appl Sci, 2013, 36: 1591-1597

[14] Yin J X, Li J, Jin C H. Non-extinction and critical exponent for a polytropic filtration equation. Nonl Anal, 2009, 71: 347-357

[15] Yin J X, Jin C H. Critical extinction and blow-up exponents for fast diffusive polytropic filtration equation with sources. Proceedings of the Edinburgh Mathematical Society, 2009, 52: 419-444

[16] Zheng P, Mu C L. Extinction and decay estimates of solutions for a polytropic filtration equation with the nonlocal source and interior absorption. Math Method Appl Sci, 2013, 36: 730-743

[17] Anderson J R. Local existence and uniqueness of solutions of degenerate parabolic equations. Commun Partial Differential Equations, 1991, 16: 105-143

CRITICAL EXTINCTION EXPONENTS FOR POLYTROPIC FILTRATION EQUATIONS WITH NONLOCAL SOURCE AND ABSORPTION

CRITICAL EXTINCTION EXPONENTS FOR POLYTROPIC FILTRATION EQUATIONS WITH NONLOCAL SOURCE AND ABSORPTION

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	刘群, 蒋达清, 史宁中, Tasawar HAYAT, Ahmed ALSAEDI. DYNAMICAL BEHAVIOR OF A STOCHASTIC HBV INFECTION MODEL WITH LOGISTIC HEPATOCYTE GROWTH[J]. 数学物理学报(英文版), 2017, 37(4): 927-940.
[2]	Kamal OULD BOUH. EXISTENCE AND NONEXISTENCE OF SOLUTIONS FOR A HARMONIC EQUATION WITH CRITICAL NONLINEARITY[J]. 数学物理学报(英文版), 2016, 36(5): 1305-1316.
[3]	张靖, 马世旺. INFINITELY MANY SIGN-CHANGING SOLUTIONS FOR THE BRÉZIS-NIRENBERG PROBLEM INVOLVING HARDY POTENTIAL[J]. 数学物理学报(英文版), 2016, 36(2): 527-536.
[4]	郑攀, 穆春来, 胡学刚, 张付臣. SECONDARY CRITICAL EXPONENT AND LIFE SPAN FOR A DOUBLY SINGULAR PARABOLIC EQUATION WITH A WEIGHTED SOURCE[J]. 数学物理学报(英文版), 2016, 36(1): 244-256.
[5]	尚月赟, 王莉. MULTIPLE NONTRIVIAL SOLUTIONS FOR A CLASS OF SEMILINEAR POLYHARMONIC EQUATIONS[J]. 数学物理学报(英文版), 2014, 34(5): 1495-1509.
[6]	王莉, 汪继秀. CRITICAL EXPONENTS AND CRITICAL DIMENSIONS FOR NONLINEAR ELLIPTIC PROBLEMS WITH SINGULAR COEFFICIENTS[J]. 数学物理学报(英文版), 2014, 34(5): 1603-1618.
[7]	孙小妹. p-LAPLACE EQUATIONS WITH MULTIPLE CRITICAL EXPONENTS AND SINGULAR CYLINDRICAL POTENTIAL[J]. 数学物理学报(英文版), 2013, 33(4): 1099-1112.
[8]	刘晓春, 梅媛. EXISTENCE OF NODAL SOLUTION FOR SEMI-LINEAR ELLIPTIC EQUATIONS WITH CRITICAL SOBOLEV EXPONENT ON SINGULAR#br# MANIFOLD[J]. 数学物理学报(英文版), 2013, 33(2): 543-555.
[9]	丁凌, 唐春雷. POSITIVE SOLUTIONS FOR CRITICAL QUASILINEAR ELLIPTIC EQUATIONS WITH MIXED DIRICHLET-NEUMANN BOUNDARY CONDITIONS[J]. 数学物理学报(英文版), 2013, 33(2): 443-470.
[10]	凌征球*, 王泽佳, 张国强. THE SIMULTANEOUS AND NON-SIMULTANEOUS BLOW-UP CRITERIA FOR A DIFFUSION SYSTEM[J]. 数学物理学报(英文版), 2013, 33(1): 139-149.
[11]	尹景学, 金春花, 杨莹. CRITICAL EXPONENTS OF EVOLUTIONARY p-LAPLACIAN WITH INTERIOR AND BOUNDARY SOURCES[J]. 数学物理学报(英文版), 2011, 31(3): 778-790.
[12]	康东升. SOLUTIONS FOR THE QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL HARDY--SOBOLEV EXPONENTS[J]. 数学物理学报(英文版), 2010, 30(5): 1529-1540.
[13]	王伟刚, 李燕, 胡迪鹤. EXTINCTION OF POPULATION-SIZE-DEPENDENT BRANCHING CHAINS IN RANDOM ENVIRONMENTS[J]. 数学物理学报(英文版), 2010, 30(4): 1065-1072.
[14]	曾宪忠, 刘振海. EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC#br# EQUATIONS IN EXTERIOR DOMAINS[J]. 数学物理学报(英文版), 2010, 30(3): 713-725.
[15]	王路生, 尹景学, 王泽佳. LARGE TIME BEHAVIOR OF SOLUTIONS TO NEWTONIAN FILTRATION EQUATIONS WITH SOURCES[J]. 数学物理学报(英文版), 2010, 30(3): 968-974.