Math @ Duke

Publications [#320452] of Stephanos Venakides
Papers Published
 Venakides, S, The zero dispersion limit of the korteweg‐de vries equation for initial potentials with non‐trivial reflection coefficient,
Communications on Pure & Applied Mathematics, vol. 38 no. 2
(January, 1985),
pp. 125155 [doi]
(last updated on 2017/12/12)
Abstract: The inverse scattering method is used to determine the distribution limit as ϵ → 0 of the solution u(x, t, ϵ) of the initial value problem. U t − 6uu x + ϵ 2 u xxx = 0, u(x, 0) = v(x), where v(x) is a positive bump which decays sufficiently fast as x x→±α. The case v(x) ≪ 0 has been solved by Peter D. Lax and C. David Levermore [8], [9] , [10]. The computation of the distribution limit of u(x, t, ϵ) as ϵ → 0 is reduced to a quadratic maximization problem, which is then solved. Copyright © 1985 Wiley Periodicals, Inc., A Wiley Company


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