Glasnik Matematicki, Vol. 46, No.1 (2011), 215-231.
THE CAUCHY PROBLEM FOR ONE-DIMENSIONAL FLOW OF A COMPRESSIBLE VISCOUS
FLUID: STABILIZATION OF THE SOLUTION
Nermina Mujaković and Ivan Dražić
Department of Mathematics, University of Rijeka, Omladinska 14, 51 000 Rijeka, Croatia
Faculty of Engineering, University of Rijeka, Vukovarska 58, 51 000 Rijeka, Croatia
Abstract. We analyze the Cauchy problem for non-stationary 1-D flow
of a compressible viscous and heat-conducting fluid, assuming that it is in the thermodynamical sense perfect and polytropic. This problem has a
unique generalized solution on R × ]0,T[ for each T>0. Supposing that the initial functions are small perturbations of
the constants and using some a priori estimates for the solution independent of T, we prove a stabilization of the solution.
2000 Mathematics Subject Classification.
46E35, 35B40, 35B45, 76N10.
Key words and phrases. Compressible viscous fluid, the Cauchy problem, stabilization.
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