## Asymptotics of reaction-diffusion equations.(Russian)Zbl 0695.35101

Consider the Cauchy problem for the reaction-diffusion equation $\epsilon \partial u/\partial t-\epsilon^ 2(\partial /\partial x)(\lambda (x,t)\partial u/\partial x)-\gamma (x,t)F(u)=0,$
$u=u(x,t,\epsilon)_{t=0}=\psi (x/\epsilon,x),\quad \lambda,\gamma \geq \delta >0,\quad \lambda,\gamma f\in C^{\infty}.$ The existence of asymptotics of solution of this problem is proved.
Reviewer: J.H.Tian

### MSC:

 35K57 Reaction-diffusion equations 35B40 Asymptotic behavior of solutions to PDEs

### Keywords:

Cauchy problem; asymptotics