Stabilization for equations of one-dimensional viscous compressible heat-conducting media with nonmonotone equation of state

[摘要] We consider the Navier-Stokes system describing motions of viscous compressible heat-conducting and self-gravitating media. We use the state function of the form p(u, theta) = p(0)(u) + p(1) (u)theta linear with respect to the temperature theta, but we admit rather general nonmonotone functions p(0) and p(1) of u, which allows us to treat various physical models of nuclear fluids (for which p and u are the pressure and the specific volume) or thermoviscoelastic solids. For solutions to an associated initial-boundary value problem with fixed-free boundary conditions and arbitrarily large data, we prove a collection of estimates independent of time interval, including uniform two-sided bounds for u, and describe asymptotic behavior as t --> infinity. Namely, we establish the stabilization pointwisely and in L-q for u, in L-2 for theta, and in L-q for v (the velocity), for any q epsilon [2, infinity). For completeness, the proof of the corresponding global existence theorem is also included. (C) 2003 Elsevier Inc. All rights reserved.

[发布日期] 2003-10-10

[关键词] stabilization;large data;viscous compressible heat-conducting fluid;thermoviscoelastic solid;nonmonotone equation of state