Asymptotic Behavior of Solutions Toward a Multiwave Pattern to the Cauchy Problem for the Scalar Conservation Law with the Ostwald--de Waele-Type Viscosity

DOI10.1137/16M1090491zbMath1377.35152arXiv1411.6332MaRDI QIDQ5270341

Natsumi Yoshida

Publication date: 23 June 2017

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.6332

zbMATH Keywords

asymptotic behaviorviscous conservation lawrarefaction waveviscous contact wavemultiwave pattern\(p\)-Laplacian-type degenerate viscosityOstwald-de Waele-type viscositypartially linearly degenerate flux

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Hyperbolic conservation laws (35L65)

Related Items (11)

Asymptotic behavior of solutions toward the rarefaction waves to the Cauchy problem for the generalized Benjamin–Bona–Mahony–Burgers equation with dissipative term ⋮ Time decay rate of solutions toward the viscous shock waves to the Cauchy problem for the scalar conservation law with nonlinear viscosity and discontinuous initial data ⋮ Decay properties of solutions toward a multiwave pattern to the Cauchy problem for the scalar conservation law with degenerate flux and viscosity ⋮ Global asymptotics toward the rarefaction waves for solutions to the Cauchy problem of the scalar conservation law with nonlinear viscosity ⋮ Decay properties of solutions to the Cauchy problem for the scalar conservation law with nonlinearly degenerate viscosity ⋮ Asymptotic behavior of solutions toward the constant state to the Cauchy problem for the non-viscous diffusive dispersive conservation law ⋮ Asymptotic Behavior of Solutions Toward the Viscous Shock Waves to the Cauchy Problem for the Scalar Conservation Law with Nonlinear Flux and Viscosity ⋮ Global structure of solutions toward the rarefaction waves for the Cauchy problem of the scalar conservation law with nonlinear viscosity ⋮ Global asymptotic stability of the rarefaction waves to the Cauchy problem for the scalar non-viscous diffusive dispersive conservation laws ⋮ Time decay rate of solutions toward the viscous shock waves under periodic perturbations for the scalar conservation law with nonlinear viscosity ⋮ Asymptotic behavior of solutions toward the rarefaction waves to the Cauchy problem for the scalar diffusive dispersive conservation laws

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