Universal attractors for a nonlinear one-dimensional heat-conductive viscous real gas

Yuming Qin; Jaime E. Muñoz Rivera

doi:10.1017/S0308210500001840

Abstract

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In this paper we employ some new ideas and more delicate estimates, as well as some ideas from previous works, to establish the existence of universal attractors for a nonlinear one-dimensional heat-conductive viscous real gas in the bounded domain Ω = (0,1).

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Qin, Yuming 2004. Universal attractor inH4for the nonlinear one-dimensional compressible Navier–Stokes equations. Journal of Differential Equations, Vol. 207, Issue. 1, p. 21.

Qin, Yuming and Fang, Jianan 2006. Global attractor for a nonlinear thermoviscoelastic model with a non-convex free energy density. Nonlinear Analysis: Theory, Methods & Applications, Vol. 65, Issue. 4, p. 892.

Qin, Yuming Huang, Lan and Yao, Zheng-an 2008. Regularity of 1D compressible isentropic Navier–Stokes equations with density-dependent viscosity. Journal of Differential Equations, Vol. 245, Issue. 12, p. 3956.

QIN, YUMING and ZHAO, YANLI 2008. GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE COMPRESSIBLE NAVIER–STOKES EQUATIONS FOR A 1D ISOTHERMAL VISCOUS GAS. Mathematical Models and Methods in Applied Sciences, Vol. 18, Issue. 08, p. 1383.

Qin, Yuming and Lü, Tzon-Tzer 2008. Global attractor for a nonlinear viscoelastic model. Journal of Mathematical Analysis and Applications, Vol. 341, Issue. 2, p. 975.

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QIN, YUMING and HUANG, LAN 2010. REGULARITY AND EXPONENTIAL STABILITY OF THE pth NEWTONIAN FLUID IN ONE SPACE DIMENSION. Mathematical Models and Methods in Applied Sciences, Vol. 20, Issue. 04, p. 589.

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Qin, Yuming and Huang, Lan 2010. Global existence and exponential stability for the th power viscous reactive gas. Nonlinear Analysis: Theory, Methods & Applications, Vol. 73, Issue. 9, p. 2800.

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Qin, Yuming and Jiang, Limin 2010. Global existence and exponential stability of solutions inH4for the compressible Navier–Stokes equations with the cylinder symmetry. Journal of Differential Equations, Vol. 249, Issue. 6, p. 1353.

Qin, Yuming Yang, Xinguang and Liu, Xin 2012. Averaging of a 3D Navier–Stokes–Voight equation with singularly oscillating forces. Nonlinear Analysis: Real World Applications, Vol. 13, Issue. 2, p. 893.

Jiang, Jie and Zheng, Songmu 2012. Global solvability and asymptotic behavior of a free boundary problem for the one-dimensional viscous radiative and reactive gas. Journal of Mathematical Physics, Vol. 53, Issue. 12,

Yuming, Qin Xinguang, Yang and Xin, Liu 2012. Pullback attractors for the non-autonomous Benjamin-Bona-Mahony equations in H2. Acta Mathematica Scientia, Vol. 32, Issue. 4, p. 1338.

Qin, Yuming Zhang, Jianpeng and Sun, Linlin 2013. Upper semicontinuity of pullback attractors for a non-autonomous viscoelastic equation. Applied Mathematics and Computation, Vol. 223, Issue. , p. 362.

Jiang, Jie and Zheng, Songmu 2014. Global well-posedness and exponential stability of solutions for the viscous radiative and reactive gas. Zeitschrift für angewandte Mathematik und Physik, Vol. 65, Issue. 4, p. 645.

Qin, Yuming Zhang, Jianlin Su, Xing and Cao, Jie 2016. Global Existence and Exponential Stability of Spherically Symmetric Solutions to a Compressible Combustion Radiative and Reactive Gas. Journal of Mathematical Fluid Mechanics, Vol. 18, Issue. 3, p. 415.

Qin, Yuming 2017. Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. p. 1.

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Universal attractors for a nonlinear one-dimensional heat-conductive viscous real gas

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