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Volume 3, Issue 2
Static Solutions of Mixed Burgers-KdV Equation II

Guan Keying

J. Part. Diff. Eq.,3(1990),pp.27-40

Published online: 1990-03

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  • Abstract
Based on the method of qualitative research in ordinary differential equations, lt is proved that, for any given positive β and ϒ, and for any given real a, b and c, the Burgers-KdV equation u_t + uu_x - ϒu_{xx} + βu_{xxx} = 0 has at least one, but at most finite Static solutions satisfying the same boundary conditions u(0, t) = a,u(1, t) = b \quad and u_x(1, t) = c on the interval [0, 1] of x. Some sufficient conditions on the global stability for certain statle solutions are given.
  • Keywords

Boundary conditions number of static solutions global stability dissipation dispersion

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@Article{JPDE-3-27, author = {Guan Keying}, title = {Static Solutions of Mixed Burgers-KdV Equation II}, journal = {Journal of Partial Differential Equations}, year = {1990}, volume = {3}, number = {2}, pages = {27--40}, abstract = { Based on the method of qualitative research in ordinary differential equations, lt is proved that, for any given positive β and ϒ, and for any given real a, b and c, the Burgers-KdV equation u_t + uu_x - ϒu_{xx} + βu_{xxx} = 0 has at least one, but at most finite Static solutions satisfying the same boundary conditions u(0, t) = a,u(1, t) = b \quad and u_x(1, t) = c on the interval [0, 1] of x. Some sufficient conditions on the global stability for certain statle solutions are given.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5796.html} }
TY - JOUR T1 - Static Solutions of Mixed Burgers-KdV Equation II AU - Guan Keying JO - Journal of Partial Differential Equations VL - 2 SP - 27 EP - 40 PY - 1990 DA - 1990/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5796.html KW - Boundary conditions KW - number of static solutions KW - global stability KW - dissipation KW - dispersion AB - Based on the method of qualitative research in ordinary differential equations, lt is proved that, for any given positive β and ϒ, and for any given real a, b and c, the Burgers-KdV equation u_t + uu_x - ϒu_{xx} + βu_{xxx} = 0 has at least one, but at most finite Static solutions satisfying the same boundary conditions u(0, t) = a,u(1, t) = b \quad and u_x(1, t) = c on the interval [0, 1] of x. Some sufficient conditions on the global stability for certain statle solutions are given.
Guan Keying. (1970). Static Solutions of Mixed Burgers-KdV Equation II. Journal of Partial Differential Equations. 3 (2). 27-40. doi:
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