Asymptotic Behavior of Solutions to the Cauchy Problem for the Scalar Viscous Conservation Law with Partially Linearly Degenerate Flux

DOI10.1137/110839448zbMath1255.35048OpenAlexW2091424227MaRDI QIDQ3165285

Natsumi Yoshida, Akitaka Matsumura

Publication date: 26 October 2012

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

Full work available at URL: https://doi.org/10.1137/110839448

zbMATH Keywords

multiwave patternrarefaction wave, viscous contact wave

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Degenerate parabolic equations (35K65) Hyperbolic conservation laws (35L65) Initial value problems for second-order parabolic equations (35K15) Initial value problems for first-order hyperbolic equations (35L03)

Related Items (10)

Asymptotic behavior of solutions toward the rarefaction waves to the Cauchy problem for the generalized Benjamin–Bona–Mahony–Burgers equation with dissipative term ⋮ 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 ⋮ Asymptotic behavior of solutions toward the rarefaction waves to the Cauchy problem for the scalar diffusive dispersive conservation laws ⋮ Asymptotic Behavior of Solutions Toward a Multiwave Pattern to the Cauchy Problem for the Scalar Conservation Law with the Ostwald--de Waele-Type Viscosity

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