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

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dc.creatorDucomet, Bernard
dc.creatorZlotnik, Alexander
dc.date2002-06-05
dc.date.accessioned2026-07-07T04:29:14Z
dc.date.available2026-07-07T04:29:14Z
dc.descriptionWe consider the Navier-Stokes system describing motions of viscous compressible heat-conducting and "self-gravitating" media. We use the state function of the form $p(η,θ)=p_0(η)+p_1(η)θ$ linear with respect to the temperature $θ$, but we admit rather general nonmonotone functions $p_0$ and $p_1$ of $η$, which allows us to treat various physical models of nuclear fluids (for which $p$ and $η$ are the pressure and specific volume) or thermoviscoelastic solids. For an associated initial-boundary value problem with "fixed-free" boundary conditions and possibly large data, we prove a collection of estimates independent of time interval for solutions, including two-sided bounds for $η$, together with its asymptotic behaviour as $t\to \infty$. Namely, we establish the stabilization pointwise and in $L^q$ for $η$, in $L^2$ for $θ$, and in $L^q$ for $v$ (the velocity), for any $q\in[2,\infty)$.
dc.description22 pages, Submitted to: "Journal of Differential Equations."
dc.identifierhttps://arxiv.org/abs/math-ph/0206005
dc.identifierhttp://arxiv.org/abs/math-ph/0206005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57081
dc.subjectMathematical Physics
dc.subject74D10 (Primary) 76D05; 76N15 (Secondary)
dc.titleStabilization for equations of one-dimensional viscous compressible heat-conducting media with nonmonotone equation of state
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