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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

35L60 First-order nonlinear hyperbolic equations
35B20 Perturbations in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
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