A LIOUVILLE-TYPE THEOREM FOR COOPERATIVE PARABOLIC SYSTEMS

被引：7

作者：

Anh Tuan Duong ^{[1
]}

Quoc Hung Phan ^{[2
]}

机构：

[1] Hanoi Natl Univ Educ, Dept Math, 136 Xuan Thuy St, Hanoi, Vietnam

[2] Duy Tan Univ, Inst Res & Dev, Da Nang, Vietnam

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 02期

关键词：

Liouville-type theorem; parabolic system; singularity estimate; universal estimate; blow-up rate; POSITIVE SOLUTIONS; ELLIPTIC-SYSTEMS; EQUATIONS;

D O I：

10.3934/dcds.2018035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove Liouville-type theorem for semilinear parabolic system of the form u(t) - Delta u = a(11)u(p) + a(12)u(r)v(s+1) , v(t) - Delta v = a(21)u(r+1)v(s) + a(22)v(p) where r, s > 0, p = r + s + 1. The real matrix A = (a(ij)) satisfies conditions a(12), a(21) >= 0 and a(11), a(22) > 0. This paper is a continuation of Phan-Souplet (Math. Ann., 366, 1561-1585, 2016) where the authors considered the special case s = r for the system of m components. Our tool for the proof of Liouville-type theorem is a refinement of Phan-Souplet, which is based on Gidas-Spruck (Commun. Pure Appl. Math. 34, 525-598 1981) and Bidaut-Veron (Equations aux derivees partielles et applications. Elsevier, Paris, pp 189-198, 1998).

引用

页码：823 / 833

页数：11

共 21 条

[1] AMANN H, 1985, J REINE ANGEW MATH, V360, P47
[2] A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system
Bartsch, Thomas
Dancer, E. Norman
Wang, Zhi-Qiang
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 37 (3-4) : 345 - 361
[3] Bebernes J., 1989, MATH PROBLEMS COMBUS
[4] Bidaut-Veron M.-F., 1998, Equations aux derivees partielles et applications, P189
[5] BidautVeron MF, 1996, COMMUN PART DIFF EQ, V21, P1035
[6] PERMANENCE IN ECOLOGICAL-SYSTEMS WITH SPATIAL HETEROGENEITY
CANTRELL, RS
COSNER, C
HUTSON, V
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1993, 123 : 533 - 559
[7] Uniform Holder estimate for singularly perturbed parabolic systems of Bose-Einstein condensates and competing species
Dancer, E. N.
Wang, Kelei
Zhang, Zhitao
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 251 (10) : 2737 - 2769
[8] A priori bounds versus multiple existence of positive solutions for a nonlinear Schrodinger system
Dancer, E. N.
Wei, Juncheng
Weth, Tobias
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2010, 27 (03): : 953 - 969
[9] BOUNDEDNESS AND BLOW UP FOR A SEMILINEAR REACTION DIFFUSION SYSTEM
ESCOBEDO, M
HERRERO, MA
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1991, 89 (01) : 176 - 202
[10] ON COOPERATIVE PARABOLIC SYSTEMS: HARNACK INEQUALITIES AND ASYMPTOTIC SYMMETRY
Foeldes, J.
Polacik, P.
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 25 (01) : 133 - 157

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