BLOW-UP OF THE SOLUTION FOR A CLASS OF POROUS MEDIUM EQUATION WITH POSITIVE INITIAL ENERGY

doi:10.1016/S0252-9602(13)60060-0

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (4): 1024-1030.doi: 10.1016/S0252-9602(13)60060-0

BLOW-UP OF THE SOLUTION FOR A CLASS OF POROUS MEDIUM EQUATION WITH POSITIVE INITIAL ENERGY

吴秀兰^1,2|高文杰^1*

1. Institute of Mathematics, Jilin University, Changchun 130012, China
2. College of Mathematics, Jilin Normal University, Siping 136000, China

收稿日期:2012-05-14 出版日期:2013-07-20 发布日期:2013-07-20
通讯作者: 高文杰,wjgao@jlu.edu.cn E-mail:chjlsywxl@126.com; wjgao@jlu.edu.cn
基金资助:
The project is supported by NSFC (11271154), Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education and by the 985 Program of Jilin University.

BLOW-UP OF THE SOLUTION FOR A CLASS OF POROUS MEDIUM EQUATION WITH POSITIVE INITIAL ENERGY

WU Xiu-Lan^1,2, GAO Wen-Jie^1*

1. Institute of Mathematics, Jilin University, Changchun 130012, China
2. College of Mathematics, Jilin Normal University, Siping 136000, China

Received:2012-05-14 Online:2013-07-20 Published:2013-07-20
Contact: GAO Wen-Jie,wjgao@jlu.edu.cn E-mail:chjlsywxl@126.com; wjgao@jlu.edu.cn
Supported by:
The project is supported by NSFC (11271154), Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education and by the 985 Program of Jilin University.

摘要/Abstract

摘要：

This paper deals with a class of porous medium equation
u_t= Δu^m + f(u)
with homogeneous Dirichlet boundary conditions. The blow-up criteria is established by using the method of energy under the suitable condition on the function f(u).

关键词: porous medium equation, blow-up, positive initial energy

Abstract:

Key words: porous medium equation, blow-up, positive initial energy

中图分类号:

35K55

吴秀兰, 高文杰. BLOW-UP OF THE SOLUTION FOR A CLASS OF POROUS MEDIUM EQUATION WITH POSITIVE INITIAL ENERGY[J]. 数学物理学报(英文版), 2013, 33(4): 1024-1030.

WU Xiu-Lan, GAO Wen-Jie. BLOW-UP OF THE SOLUTION FOR A CLASS OF POROUS MEDIUM EQUATION WITH POSITIVE INITIAL ENERGY[J]. Acta mathematica scientia,Series B, 2013, 33(4): 1024-1030.

参考文献

[1] Wu Z Q, Zhao J N, Yin J X, Li H L. Nonlinear Diffusion Equations. Singapore: World Scientific, 2001

[2] Galaktionov V A, Vazquez J L. The problem of blow-up in nonlinear parabolic equations. Discrete Contin Dynam System, 2002, 8(2): 399–433

[3] Ferreira R, Vazquez J L. Extinction behavior for fast diffusion equations with absorption. Nonlinear Anal, 2001, 43: 943–985

[4] Li Y X, Wu J C. Extinction for fast diffusion equations with nonlinear sources. Electron J Differ Equ, 2005, 23: 1–7

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

[6] Peietier L A, Junning Z. Source-type solutions of porous media equation with absorption: The fast diffusion case. Nonlinear Anal, 1991, 17: 991–1009

[7] Leoni G. A very singular solution for the porous media equation u_t= Δu^m− up when 0 < m < 1. J Diff Equ, 1996, 132: 353–376

[8] Mochizuki K, Suzuki R. Critical exponent and critical blow up for quasi-linear parabolic equations. Israel J Math, 1997, 98: 141–156

[9] Mu C L, Zeng R, Chen B T. Blow-up phenomena for a doubly degenerate equation with positive initial energy. Nonlinear Anal, 2010, 72: 782–793

[10] Liu W J, Wang M X. Blow-up of the solution for a p-Laplaican equation with positive initial energy. Acta Appl Math, 2008, 103: 141–146

[11] Gao W J, Han Y Z. Blow-up of a nonlocal semilinear parabolic equation with positive initial energy. Appl Math Lett, 2011, 24: 784–788

[12] Wang J, Gao W J. Existence of solutions to a class of doubly degenerate equations and blow up with vanishing intial energy. J Math Res Exposition, 2007, 27: 161–168 (in Chinese)

[13] Ladyzenskaja O, Solonnikov V, Uraltseva N. Linear and Quasilinear Equations of Parabolic Type. Transl Math Monogr. Providence, RI: American Mathematical Society, 1968

[14] Zhong C K, Fan X L, Chen W Y. Nonlinear Functinal Analysis. Lanzhou: Lanzhou University Press, 2004 (in Chinese)

[15] Vitillaro E. Global nonexistence theorems for a class of evolution equations with dissipation. Arch Ration Mech Anal, 1999, 149: 155–182

[16] Mu C L, Hu X G, Li Y H, Cui Z J. Blow-up and global existence for a coupled system of degenerate parabolic equations in a bounded domain. Acta Math Sci, 2007, 27B(1): 92–106

BLOW-UP OF THE SOLUTION FOR A CLASS OF POROUS MEDIUM EQUATION WITH POSITIVE INITIAL ENERGY

BLOW-UP OF THE SOLUTION FOR A CLASS OF POROUS MEDIUM EQUATION WITH POSITIVE INITIAL ENERGY

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]	Yue-Loong CHANG, Meng-Rong LI, C. Jack YUE, Yong-Shiuan LEE, Tsung-Jui CHIANG-LIN. MATHEMATICAL MODEL FOR THE ENTERPRISE COMPETITIVE ABILITY AND PERFORMANCE THROUGH A PARTICULAR EMDEN-FOWLER EQUATION u"-n^-q-1u (n)^q=0[J]. 数学物理学报(英文版), 2018, 38(4): 1311-1321.
[2]	林勇, 吴艺婷. BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS[J]. 数学物理学报(英文版), 2018, 38(3): 843-856.
[3]	朱新才. EXISTENCE AND BLOW-UP BEHAVIOR OF CONSTRAINED MINIMIZERS FOR SCHRÖDINGER-POISSON-SLATER SYSTEM[J]. 数学物理学报(英文版), 2018, 38(2): 733-744.
[4]	杨凌燕, 李晓光, 吴永洪, Louis CACCETTA. GLOBAL WELL-POSEDNESS AND BLOW-UP FOR THE HARTREE EQUATION[J]. 数学物理学报(英文版), 2017, 37(4): 941-948.
[5]	孔慧慧, 李海梁, 张兴伟. A BLOW-UP CRITERION OF SPHERICALLY SYMMETRIC STRONG SOLUTIONS TO 3D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY[J]. 数学物理学报(英文版), 2016, 36(4): 1153-1166.
[6]	朱圣国. BLOW-UP OF CLASSICAL SOLUTIONS TO THE COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH VACUUM[J]. 数学物理学报(英文版), 2016, 36(1): 220-232.
[7]	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.
[8]	张裕隆, 李明融. A MATHEMATICAL MODEL OF ENTERPRISE COMPETITIVE ABILITY AND PERFORMANCE THROUGH EMDEN-FOWLER EQUATION FOR SOME ENTERPRISES[J]. 数学物理学报(英文版), 2015, 35(5): 1014-1022.
[9]	李玉环, 米永生, 穆春来. PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION[J]. 数学物理学报(英文版), 2014, 34(3): 748-758.
[10]	Meng-Rong LI, Yue-Loong CHANG, Yu-Tso LI. A MATHEMATICAL MODEL OF ENTERPRISE COMPETITIVE ABILITY AND PERFORMANCE THROUGH EMDEN-FOWLER EQUATION (II)[J]. 数学物理学报(英文版), 2013, 33(4): 1127-1140.
[11]	周寿明, 穆春来, 王良展. SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM[J]. 数学物理学报(英文版), 2013, 33(3): 821-829.
[12]	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.
[13]	徐新英. A BLOW-UP CRITERION FOR 3-D NON-RESISTIVE COMPRESSIBLE HEAT-CONDUCTIVE MAGNETOHYDRODYNAMIC EQUATIONS#br# WITH INITIAL VACUUM[J]. 数学物理学报(英文版), 2012, 32(5): 1883-1900.
[14]	孔令花, 王金环, 郑斯宁. UNIFORM BLOW-UP PROFILES FOR HEAT EQUATIONS WITH COUPLING NONLOCAL SOURCES OF ASYMMETRIC MIXED TYPE#br# NONLINEARITIES[J]. 数学物理学报(英文版), 2012, 32(3): 1126-1140.
[15]	朱世辉, 张健. LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL[J]. 数学物理学报(英文版), 2012, 32(3): 1181-1192.