Stability of Equilibrium Solutions of a Nonlinear Reaction-Diffusion Equation

被引：0

作者：

Hernandez Melo, Cesar Adolfo ^{[1
]}

Demetrio, Luiz Felipe ^{[2
]}

机构：

[1] Univ Estadual Maringa, Dept Math, Maringa, Parana, Brazil

[2] Univ Estadual Maringa, Dept Phys, Maringa, Parana, Brazil

来源：

BOLETIN DE MATEMATICAS | 2020年 / 27卷 / 01期

关键词：

Reaction-Diffusion equation; equilibrium solutions; stability;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present work, it is analyzed existence and stability of equilibrium solutions of the following nonlinear reaction-diffusion equation: u(t) = Qu(xx) + wu + k ln(u(2))u. Explicit formulas for a family of equilibrium solutions to the former equation which decay to zero at infinity are provided. The instability of those solutions is obtained by detailed spectral analysis of the linear operator which approximates the solutions of the equation around the equilibrium solutions. A result about the instability of any non-trivial equilibrium solution of the equation is also established.

引用

页码：1 / 14

页数：14

共 14 条

[1] Superexponential growth or decay in the heat equation with a logarithmic nonlinearity [J].

Alfaro, Matthieu ;

Carles, Remi .

DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS, 2017, 14 (04) :343-358

[2]

[Anonymous], 2013, APPL MATH SCI, DOI DOI 10.1007/978-1-4614-6995-7

[3] The wave of advance of advantageous genes [J].

Fisher, RA .

ANNALS OF EUGENICS, 1937, 7 :355-369

[4]

Galaktionov VA, 2002, DISCRETE CONT DYN-A, V8, P399

[5] Stability of Traveling Waves in Partly Parabolic Systems [J].

Ghazaryan, A. ;

Latushkin, Y. ;

Schecter, S. .

MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2013, 8 (05) :31-47

[6]

Henry D., 1981, GEOMETRIC THEORY SEM, V840, DOI DOI 10.1007/BFB0089647

[7]

HERNANDEZ MCA, 2014, APPL MATH COMPUT, P1025

[8]

Kersner, 2012, PROGR NONLINEAR DIFF, V60

[9] Numerical modeling of wave propagation for damped elbow pipes using Fourier-Legendre spectral element method in polar coordinates [J].

Liu, Yijie ;

Han, Qiang ;

Li, Chunlei ;

Xiao, Dongliang .

ARCHIVE OF APPLIED MECHANICS, 2016, 86 (12) :1995-2008

[10] Stability of equilibrium solutions of a double power reaction-diffusion equation with a Dirac interaction [J].

Melo Hernandez, Cesar Adolfo ;

Lancheros Mayorga, Edgar Yesid .

MATHEMATISCHE NACHRICHTEN, 2020, 293 (04) :721-734

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