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Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions. (English) Zbl 1365.35192

Summary: We are interested in the evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified.

MSC:

35R02 PDEs on graphs and networks (ramified or polygonal spaces)
35L20 Initial-boundary value problems for second-order hyperbolic equations
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