Large time behavior of solutions to the generalized Burgers equations

zbMath1132.35311MaRDI QIDQ2472333

Masakazu Kato

Publication date: 21 February 2008

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ojm/1199719413

zbMATH Keywords

self-similar solutionoptimal ratesecond asymptotic profile

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Hyperbolic conservation laws (35L65) Initial value problems for second-order parabolic equations (35K15)

Related Items (15)

On group invariant solutions of fractional order Burgers-Poisson equation ⋮ Asymptotic behavior of solutions to the drift-diffusion equation with critical dissipation ⋮ Asymptotic expansion of solutions to the drift-diffusion equation with fractional dissipation ⋮ Large time behavior of solutions to the Cauchy problem for the BBM-Burgers equation ⋮ Time-asymptotic expansion with pointwise remainder estimates for 1D viscous compressible flow ⋮ Asymptotic periodic solutions of some generalized Burgers equations ⋮ Asymptotic profiles of solutions for the generalized Fornberg-Whitham equation with dissipation ⋮ Large-time behavior of solutions to the Rosenau equation with damped term ⋮ Spatial-decay of solutions to the quasi-geostrophic equation with the critical and supercritical dissipation ⋮ Higher-order asymptotic profiles of the solutions to the viscous Fornberg-Whitham equation ⋮ Analytical method for solving the fractional order generalized KdV equation by a beta-fractional derivative ⋮ Asymptotic behavior of solutions to the generalized KdV-Burgers equation ⋮ Well-posedness of the generalized Burgers equation on a finite interval ⋮ Asymptotic behavior of solutions to the generalized KdV-Burgers equation with slowly decaying data ⋮ Asymptotic expansion of solutions to the nonlinear dissipative equation with the anomalous diffusion

Cites Work

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• Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas
• Large time asymptotics for the BBM-Burgers equation
• Second term of asymptotics for KdVB equation with large initial data
• Asymptotics for the Korteweg-de Vries-Burgers equation
• Large-time behaviour of solutions to hyperbolic–parabolic systems of conservation laws and applications
• Hyperbolic and Viscous Conservation Laws
• The partial differential equation u_t + uu_x = μ_xx
• On a quasi-linear parabolic equation occurring in aerodynamics

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