Temporal asymptotic behaviour of solutions of the Benjamin-Ono-Burgers equation

DOI10.1016/0022-0396(91)90148-3zbMath0784.35098OpenAlexW1973210850MaRDI QIDQ1176493

Daniel B. Dix

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1016/0022-0396(91)90148-3

zbMATH Keywords

regularityexistenceuniquenesssimilarity solutionsBenjamin-Ono-Burgers equationspatial asymptoticsrate of decay

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (23)

Unnamed Item ⋮ Asymptotic property for the solution to the generalized Korteweg-de Vries equation ⋮ Asymptotics in the critical case for Whitham type equations ⋮ Sharp well-posedness for the Chen-Lee equation ⋮ Decay of global solutions of two nonlinear evolution equations ⋮ Differential and analytical properties of semigroups of operators ⋮ Decay of solutions of a higher order multidimensional nonlinear Korteweg–de Vries–Burgers system ⋮ The dissipation of nonlinear dispersive waves: the case of asymptotically weak nonlinearity ⋮ Decay of solutions of generalized Benjamin-Bona-Mahony equations ⋮ Decay rates of the solutions of nonlinear dispersive equations ⋮ Decay of solution of generalized Benjamin—Bona—Mahony—Burgers equations in n-space dimensions ⋮ The Cauchy problem for dissipative Benjamin-Ono equation in weighted Sobolev spaces ⋮ Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE ⋮ Uniform well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation ⋮ Well-posedness and ill-posedness results for dissipative Benjamin-Ono equations ⋮ On the Cauchy problem for nonlinear dissipative systems ⋮ Global behavior for Whitham type equations on a finite interval ⋮ Solutions to some open problems in fluid dynamics ⋮ FRACTIONAL LANDAU–GINZBURG EQUATIONS ON A SEGMENT ⋮ Asymptotics for the Korteweg-de Vries-Burgers equation ⋮ Decay estimates for the solutions of some multidimensional nonlinear evolution equations ⋮ Long time behavior of solutions for a damped Benjamin-Ono equation ⋮ Well-posedness of a semilinear heat equation with weak initial data

Cites Work

• Decay of solutions of some nonlinear wave equations
• The Benjamin-Ono-Burgers equation: An application in solar physics
• \(L^ 2\) decay for weak solutions of the Navier-Stokes equations
• On \(L^ 2\) decay of weak solutions of the Navier-Stokes equations in \(\mathbb R^ n\)
• Sur quelques généralisations de l'équation de Korteweg-de Vries
• On the cauchy problem for the benjamin-ono equation
• The partial differential equation u_t + uu_x = μ_xx
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