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Long-wave asymptotics of the solution of a hyperbolic system of equations. (Russian) Zbl 0566.35066
The long-wave asymptotics of the solution U(x,t,$$\epsilon)$$ at $$\epsilon$$ $$\to 0$$ of the hyperbolic system of equations $[\partial_ t+\lambda_ i(\xi,\tau)\partial_ x]u_ i=\epsilon [A_ i(U,\epsilon,\tau)\partial_ xU+b_ i(U,\xi,\tau)]$ with initial conditions $$u_ i(x,t,\epsilon)|_{t=0}=\phi_ i(x,\xi),$$ $$i=1,...,m$$ uniformly in some region $$0\leq | x| +t\leq M\epsilon^{-1}$$ are constructed. Here x,t are independent variables, $$x\in R^ 1$$, $$t\geq 0$$ is a small parameter; $$\xi =\epsilon x$$, $$\tau =\epsilon t$$ are slow variables; $$\lambda_ i(\xi,\tau)$$ are scalar functions; $$b_ i$$, $$\phi_ i$$ are known and $$u_ i$$ unknown functions.
Reviewer: L.G.Vulkov

##### MSC:
 35L60 First-order nonlinear hyperbolic equations 35B20 Perturbations in context of PDEs 35B40 Asymptotic behavior of solutions to PDEs
##### Keywords:
long-wave asymptotics; small parameter
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