#### 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

*e-mail:* `mujakovic@inet.hr`

Faculty of Engineering, University of Rijeka, Vukovarska 58, 51 000 Rijeka, Croatia

*e-mail:* `idrazic@riteh.hr`

**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.

**Full text (PDF)** (access from subscribing institutions only)
DOI: 10.3336/gm.46.1.16

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