On the critical set for discrete Laplacian parabolic equations with polynominal-type reactions

被引：0
|
作者：
Chung, Soon-Yeong [1 ,2 ]
Choi, Min-Jun [3 ]
Hwang, Jaeho [2 ,4 ]
机构：
[1] Natl Inst Math Sci, Daejeon, South Korea
[2] Sogang Univ, Dept Math, Seoul 04107, South Korea
[3] Seoul Natl Univ, Dept Math Sci, Seoul, South Korea
[4] Sogang Univ, Res Inst Basic Sci, Seoul 04107, South Korea
来源：
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2020年 / 26卷 / 06期
关键词：
Parabolic equation; discrete Laplacian; polynomial; Fujita-type blow-up; critical set; BLOW-UP; DIFFUSION-EQUATIONS; CRITICAL EXPONENT;
D O I：
10.1080/10236198.2020.1790538
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study long-time behaviours of solutions to the discrete reaction-diffusion equations u(t) = Delta(omega)u + psi(t)f(u) with nontrivial and nonnegative initial data, under the mixed boundary conditions. In particular, the function f satisfies alpha (u(q) + u(p)) <= f(u) <= beta (u(q) + u(p)) for some constants 0 < alpha <= beta and positive real numbers p and q. The purpose of this paper is to introduce a critical set Lambda(psi) depending on the nonnegative continuous function psi. Also, we discuss about Fujita-type blow-up, which depends on the critical set Lambda(psi).
引用
收藏
页码：779 / 801
页数：23
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