Pointwise estimates and \(L_p\) convergence rates to diffusion waves for \(p\)-system with damping.

DOI10.1016/S0022-0396(02)00056-6zbMath1035.35077OpenAlexW1976342131MaRDI QIDQ1864658

Weike Wang, Tong Yang

Publication date: 18 March 2003

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-0396(02)00056-6

zbMATH Keywords

asymptotic behaviorCauchy problemnonlinear diffusion waves\(2\times 2\) system\(p\)-system with frictional dampingliner right-hand side

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Initial value problems for first-order hyperbolic systems (35L45)

Related Items (21)

Asymptotic behavior of solutions to bipolar Euler-Poisson equations with time-dependent damping ⋮ The strong relaxation limit of the multidimensional Euler equations ⋮ Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane ⋮ \(L^p-L^q\) decay estimates of solutions to Cauchy problems of thermoviscoelastic systems ⋮ Convergence rates to the Barenblatt solutions for the compressible Euler equations with time-dependent damping ⋮ Time-asymptotic expansion with pointwise remainder estimates for 1D viscous compressible flow ⋮ The \(L^{p}\)--\(L^{q}\) estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media ⋮ Large time behavior of solutions of the bipolar hydrodynamical model for semiconductors. ⋮ The best asymptotic profile of solutions to Euler equations with time‐dependent damping ⋮ Convergence to diffusion waves for solutions of 1D Keller–Segel model ⋮ Pointwise estimates and \(L^p\) convergence rates to diffusion waves for a one-dimensional bipolar hydrodynamic model ⋮ Convergence to diffusion waves for solutions of Euler equations with time-depending damping on quadrant ⋮ Existence and stability of planar diffusion waves for 2D Euler equations with damping ⋮ Convergence to nonlinear diffusion waves for solutions of Euler-Korteweg equations with damping ⋮ Convergence to nonlinear diffusion waves for solutions of \(p\)-system with time-dependent damping ⋮ Convergence to nonlinear diffusion waves for solutions of Euler equations with time-depending damping ⋮ Best asymptotic profile for linear damped \(p\)-system with boundary effect ⋮ Pointwise time asymptotic behavior of solutions to a general class of hyperbolic balance laws ⋮ \(L^p\) convergence rates of planar waves for multi-dimensional Euler equations with damping ⋮ The pointwise estimates of solutions for a model system of the radiating gas in multi-dimensions ⋮ Nonlinear diffusion waves for hyperbolic \(p\)-system with nonlinear damping

Cites Work

• The one-dimensional Darcy's law as the limit of a compressible Euler flow
• Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping
• Hyperbolic to parabolic relaxation theory for quasilinear first order systems
• Convergence rates to nonlinear diffusion waves for solutions of system of hyperbolic conservation laws with damping
• A system of hyperbolic conservation laws with frictional damping
• Compressible flow with damping and vacuum
• Gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation
• Asymptotic behavior of the solutions to the damped compressible Euler equations with vacuum
• Large time behavior of solutions for general quasilinear hyperbolic-parabolic systems of conservation laws
• Global smooth solution for nonlinearly damped_p-system with large initial data
• Global Existence of Solutions for the System of Compressible Adiabatic Flow through Porous Media
• The pointwise estimates of solutions for Euler equations with damping in multi-dimensions

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