A NON-HOMOGENEOUS BOUNDARY VALUE PROBLEM OF THE SIXTH ORDER BOUSSINESQ EQUATION IN A QUARTER PLANE.
In: Discrete & Continuous Dynamical Systems: Series A, Jg. 38 (2018-05-01), Heft 5, S. 2505-2525
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Zugriff:
The paper is concerned with an initial-boundary-value problem of the sixth order Boussinesq equation posed on a quarter plane with nonhomogeneous boundary conditions: {u tt - u xx + βu xxxx -u xxxxxx +(u 2 ) xx = 0, for x > 0, t > 0,u(x, 0) = φ(x), ut(x, 0) = ψ''(x), u(0, t) = h 1 (t), u xx (0, t) = h 2 (t), u xxxx (0, t) = h 3 (t), (1) where β = ±1. It is shown that the problem is locally well-posed in the space H s (R + ) for any 0 ⩽ s < 13/2 with the initial data (φψ ) in the space H s (R + ) × H s-1 (R + ) and the naturally compatible boundary data h 1 ∊ H s+1/3 loc (R + ), h 2 ∊ H s-1/3 loc (R + ) and h 3 ∊ H s-3/3 loc (R + ) with optimal regularity. [ABSTRACT FROM AUTHOR]
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Titel: |
A NON-HOMOGENEOUS BOUNDARY VALUE PROBLEM OF THE SIXTH ORDER BOUSSINESQ EQUATION IN A QUARTER PLANE.
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Autor/in / Beteiligte Person: | Li, Shenghao ; Chen, Min ; Zhang, Bing-Yu |
Zeitschrift: | Discrete & Continuous Dynamical Systems: Series A, Jg. 38 (2018-05-01), Heft 5, S. 2505-2525 |
Veröffentlichung: | 2018 |
Medientyp: | academicJournal |
ISSN: | 1078-0947 (print) |
DOI: | 10.3934/dcds.2018104 |
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