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

Danilov, V. G.; Maslov, V. P.

Mat. Zametki 44, No. 1, 152-153 (1988).

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