Global existence and blowup for a degenerate parabolic equation with a free boundary

被引：0

作者：

Chen, Youpeng ^{[1
]}

Liu, Xingying ^{[2
]}

机构：

[1] Nanjing Normal Inst Special Educ, Sch Math & Informat Sci, Nanjing 210038, Peoples R China

[2] Yancheng Normal Univ, Sch Math & Stat, Yancheng 224002, Peoples R China

来源：

ANNALES POLONICI MATHEMATICI | 2020年 / 124卷 / 01期

关键词：

degenerate parabolic equation; free boundary; blowup; global fast solution; global slow solution; INSTABILITY; STABILITY; BEHAVIOR; GROWTH; SYSTEM; MODEL;

D O I：

10.4064/ap171230-26-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with a free boundary problem for a degenerate parabolic equation. For such a problem, we mainly study the blowup property and global existence of solutions. Our results show that blowup occurs if the initial datum is sufficiently large, while the solution is global and fast if the initial data is sufficiently small, and that the existence of a global slow solution is possible when the initial data is suitably large.

引用

页码：1 / 31

页数：31

共 31 条

[11] SPREADING-VANISHING DICHOTOMY IN THE DIFFUSIVE LOGISTIC MODEL WITH A FREE BOUNDARY [J].

Du, Yihong ;

Lin, Zhigui .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2010, 42 (01) :377-405

[12]

FASANO A, 1979, J MATH ANAL APPL, V72, P247, DOI 10.1016/0022-247X(79)90287-7

[13]

Fila M., 2001, Interfaces Free Bound., V3, P337

[14] ANALYSIS OF A MATHEMATICAL MODEL OF ISCHEMIC CUTANEOUS WOUNDS [J].

Friedman, Avner ;

Hu, Bei ;

Xue, Chuan .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2010, 42 (05) :2013-2040

[15] Decay of global solutions, stability and blowup for a reaction-diffusion problem with free boundary [J].

Ghidouche, H ;

Souplet, P ;

Tarzia, D .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (03) :781-792

[16]

Guyonne V, 2007, DISCRETE CONT DYN-B, V7, P315

[17] Vanishing latent heat limit in a Stefan-like problem arising in biology [J].

Hilhorst, D ;

Mimura, M ;

Schätzle, R .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2003, 4 (02) :261-285

[18] ON GROWTH OF SOLUTIONS OF QUASI-LINEAR PARABOLIC EQUATIONS [J].

KAPLAN, S .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1963, 16 (03) :305-&

[19] A free boundary problem for a parabolic system describing an ecological model [J].

Kim, Kwang Ik ;

Lin, Zhigui .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2009, 10 (01) :428-436

[20] Global existence and blowup of solutions to a free boundary problem for mutualistic model [J].

Kim, KwangIk ;

Lin ZhiGui ;

Ling Zhi .

SCIENCE CHINA-MATHEMATICS, 2010, 53 (08) :2085-2095

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