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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
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