TY - JOUR

T1 - Korteweg-de Vries-Burgers equation on a half-line with large initial data

AU - Hayashi, Nakao

AU - Kaikina, Elena I.

AU - Ruiz Paredes, Hector F.

N1 - Funding Information:
The authors would like to thank the referee for useful comments. The work of E.I.K. is supported by Projects of COSNET and CONACYT.

PY - 2002

Y1 - 2002

N2 - We study the following initial-boundary value problem for the Korteweg-de Vries-Burgers equation equation presented We prove that if the initial data u0 ∈ H0,ω ∩ H0,ω, where ω ∈ (1/2, 3/2), then there exists a unique solution u ∈ C ([0,∞), H1,ω) of the initial-boundary value problem (0.1). Moreover if the initial data are such that x1+μu0(x) ∈ L1, μ = ω - 1/2, then there exists a constant A such that the solution has the following asymptotics equation presented for t → ∞ uniformly with respect to x > 0.

AB - We study the following initial-boundary value problem for the Korteweg-de Vries-Burgers equation equation presented We prove that if the initial data u0 ∈ H0,ω ∩ H0,ω, where ω ∈ (1/2, 3/2), then there exists a unique solution u ∈ C ([0,∞), H1,ω) of the initial-boundary value problem (0.1). Moreover if the initial data are such that x1+μu0(x) ∈ L1, μ = ω - 1/2, then there exists a constant A such that the solution has the following asymptotics equation presented for t → ∞ uniformly with respect to x > 0.

KW - Dissipative Nonlinear Evolution Equation

KW - Korteweg-de Vries-Burgers equation

KW - Large Time Asymptotics

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U2 - 10.1007/s00028-002-8091-0

DO - 10.1007/s00028-002-8091-0

M3 - Article

AN - SCOPUS:0346367652

VL - 2

SP - 319

EP - 347

JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

SN - 1424-3199

IS - 3

ER -