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The Cauchy Problem of a Shallow Water Equation

Acta Mathematica Sinica, English Series, 2004
The authors consider the initial value problem for a fifth order shallow water equation in the nonperiodic case, as opposed to the previously considered periodic case. The equation studied has the same nonlinear terms as the well-known Fuchssteiner-Fokas-Camassa-Holm equation, and in this sense can be considered to be a higher order analogue of this ...
Liu, Xiaofeng, Jin, Yongyang
exaly   +2 more sources

On the weak solutions to a shallow water equation

Communications on Pure and Applied Mathematics, 2000
The authors obtain the existence of global-in-time weak solutions to the Cauchy problem for a one-dimensional formally integrable shallow-water equation of Camassa-Holm type. First, for an approximate viscous problem they establish uniform in viscosity energy estimates for the solution and its gradient.
Z. Xin, Ping Zhang
semanticscholar   +3 more sources

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