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A linear homogenization problem with time dependent coefficient. (English) Zbl 0536.45003

The initial value problem \[ \partial u_{\epsilon}(x,t)/\partial t+b(x/\epsilon,t)u_{\epsilon}(x,t)=0,\quad u_{\epsilon}(x,0)=f(x) \] where \(\epsilon>0\) is a small parameter, is reduced to an equivalent integral equation. Conditions for existence and uniqueness of the kernel of the latter equation are given provided that b(x,t) is periodic in x, uniformly positive, and has a bounded derivative in t.
Reviewer: D.Bainov

MSC:

45A05 Linear integral equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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References:

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