Volkova, E. I. Asymptotics of the solution of a mixed problem for a system of differential equations connected to a positive integral operator. (Russian) Zbl 0655.60051 Mat. Sb., N. Ser. 137(179), No. 1(9), 65-75 (1988). The author considers a mixed boundary value problem for the following system of hyperbolic-type partial differential equations \[ \partial u_ i(x,t)/\partial t+\delta \quad ib_ i(x)\partial u_ i(x,t)/\partial x- \sum^{N}_{k=1}a\quad k_ i(x)u\quad_ k(x,t)=f_ i(x,t),\quad x\in [a,b],\quad t\geq 0,\quad i=1,2,...,N. \] Utilizing both the connection of this system with the functionals of branching processes with a finite number of particles and the Laplace transform the asymptotic behavior of the solutions \(\{u_ i(x,t)\}\) is obtained for \(t\to \infty\). Particularly the first term of the asymptotic expansion is written out explicitly. Reviewer: A.Dorogovtsev Cited in 1 Review MSC: 60H99 Stochastic analysis 35M99 Partial differential equations of mixed type and mixed-type systems of partial differential equations 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.) Keywords:mixed boundary value problem; branching processes; Laplace transform; asymptotic expansion PDFBibTeX XMLCite \textit{E. I. Volkova}, Mat. Sb., Nov. Ser. 137(179), No. 1(9), 65--75 (1988; Zbl 0655.60051) Full Text: EuDML