Stability of equilibrium solutions of a double power reaction-diffusion equation with a Dirac interaction

被引：1
|
作者：
Melo Hernandez, Cesar Adolfo [1 ]
Lancheros Mayorga, Edgar Yesid [2 ]
机构：
[1] Univ Estadual Maringa, Dept Math, Av Colombo 5790, BR-87020900 Maringa, Parana, Brazil
[2] Univ Sabana, Fac Engn Fis & Matemat, Aplicadas Res Grp, Chia, Cundinamarca, Colombia
来源：
MATHEMATISCHE NACHRICHTEN | 2020年 / 293卷 / 04期
关键词：
analytic perturbation theory; blow-up of solutions; Dirac distribution; reaction-diffusion equation; stability of equilibrium solutions; NONLINEAR SCHRODINGER-EQUATION; WAVE SOLUTIONS; HUXLEY;
D O I：
10.1002/mana.201700447
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, information about the instability of equilibrium solutions of a nonlinear family of localized reaction-diffusion equations in dimension one is provided. More precisely, explicit formulas to the equilibrium solutions are computed and, via analytic perturbation theory, the exact number of positive eigenvalues of the linear operator associated to the stability problem is analyzed. In addition, sufficient conditions for blow up of the solutions of the equation are also discussed.
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页码：721 / 734
页数：14
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