TY - JOUR

T1 - Large time asymptotics for the BBM-burgers equation

AU - Hayashi, Nakao

AU - Kaikina, Elena I.

AU - Naumkin, Pavel I.

N1 - Funding Information:
The work of E. I. Kaikina and P. I. Naumkin is partially supported by CONACYT. We are grateful to unknown referees for many useful suggestions and comments.

PY - 2007/6

Y1 - 2007/6

N2 - We study large time asymptotics of solutions to the BBM-Burgers equation ∂t (u - uxx) + βux - μu xx + uux = 0. We are interested in the large time asymptotics for the case, when the initial data have an arbitrary size. Let the initial data u0 ∈ H1 (R) ∩ W1 1 (R), and θ = ∫R u0 (x) dx ≠ 0. Then we prove that there exists a unique solution u(t, x) ∈ C ([0,\∞); H1 (R) ∩ W11 (R) to the Cauchy problem for the BBM-Burgers equation. We also find the large time asymptotics for the solutions.

AB - We study large time asymptotics of solutions to the BBM-Burgers equation ∂t (u - uxx) + βux - μu xx + uux = 0. We are interested in the large time asymptotics for the case, when the initial data have an arbitrary size. Let the initial data u0 ∈ H1 (R) ∩ W1 1 (R), and θ = ∫R u0 (x) dx ≠ 0. Then we prove that there exists a unique solution u(t, x) ∈ C ([0,\∞); H1 (R) ∩ W11 (R) to the Cauchy problem for the BBM-Burgers equation. We also find the large time asymptotics for the solutions.

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U2 - 10.1007/s00023-006-0314-4

DO - 10.1007/s00023-006-0314-4

M3 - Article

AN - SCOPUS:34547370636

SN - 1424-0637

VL - 8

SP - 485

EP - 511

JO - Annales Henri Poincare

JF - Annales Henri Poincare

IS - 3

ER -