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Unique solvability of the periodic Cauchy problem for wave-hierarchy problems with dissipation

✍ Scribed by Manfred F. Göz

Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
894 KB
Volume
17
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

Wave‐hierarchy problems appear in a variety of applications such as traffic flows, roll waves down an open inclined channel and multiphase flows. Usually, these are described by the compressible Navier‐Stokes equations with specific non‐linearities; in a fluidized bed model they contain an additional pressure gradient term and are supplemented by an elliptic equation for this unknown pressure. These equations admit solutions periodic in space as well as in time, i.e. periodic travelling waves. Therefore, the corresponding initial value problem with periodic boundary conditions is solved locally in time in appropriate Sobolev spaces. Some remarks are made concerning global solutions, the occurrence of clusters or voids and the bifurcation of time periodic solutions, respectively.

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## Abstract In this paper we prove the existence of global decaying __H__^2^ solutions to the Cauchy problem for a wave equation with a nonlinear dissipative term by constructing a stable set in __H__^1^(ℝ^__n__^ ). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)