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Zbl 1010.39004
Chen, Xinfu; Guo, Jong-Shenq
Existence and asymptotic stability of traveling waves of discrete quasilinear monostable equations. (English)
[J] J. Differ. Equations 184, No.2, 549-569 (2002). ISSN 0022-0396

The authors study the existence and asymptotic stability of traveling waves $$\dot u_j= [g(u_{j+1})+ q(u_{j-1})- 2g(u_j)]+ f(u_j),\tag{$*$}$$ where $j$ is an integer. By a traveling wave to $(*)$ with speed $c> 0$ they mean a solution to $(*)$ satisfying $u_j(1/c)= u_{j-1}(0)$ for all $j$. Of particular interest are the cases $g(u)= du^p$ with $d> 0$, $p\ge 1$ and $f(u)= u- u^2$.
[Kenneth S.Miller (Rye Brook)]

MSC 2000:: *39A12 Discrete version of topics in analysis
39A11 Stability of difference equations
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations

Keywords: discrete quasilinear monostable equations; asymptotic stability; traveling waves

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