Uniform boundedness of the solutions for a one-dimensional isentropic model system of compressible viscous gas |
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Authors: | Akitaka Matsumura Shigenori Yanagi |
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Institution: | (1) Department of Mathematics, Faculty of Science, Osaka University, 560 Toyonaka, Japan;(2) Department of Mathematics, Faculty of Science, Ehime University, 790 Matsuyama, Japan |
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Abstract: | This paper studies an initial boundary value problem for a one-dimensional isentropic model system of compressible viscous gas with large external forces, represented by v
t
–u
x
=0,u
t
+(av
–)
x
=(u
x
/v)
x
+f(
0
x
vdx,t), with (v(x, 0),u(x, 0))= (v
0(x),u
0(x)),u(0,t)=u(1,t)=0. Especially, the uniform boundedness of the solution in time is investigated. It is proved that for arbitrary large initial data and external forces, the problem uniquely has an uniformly bounded, global-in-time solution with also uniformly positive mass density, provided the adiabatic constant (>1) is suitably close to 1. The proof is based on L
2-energy estimates and a technique used in 9]. |
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Keywords: | |
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