Displaying similar documents to “Hyperbolic parabolic equations with nonlinearity of Kirchhoff-Carrier type.”

Remarks on the equatorial shallow water system

Chloé Mullaert (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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This article recalls the results given by A. Dutrifoy, A. Majda and S. Schochet in [1] in which they prove an uniform estimate of the system as well as the convergence to a global solution of the long wave equations as the Froud number tends to zero. Then, we will prove the convergence with weaker hypothesis and show that the life span of the solutions tends to infinity as the Froud number tends to zero.

Halfway to a solution of X 2 - D Y 2 = - 3

R. A. Mollin, A. J. Van der Poorten, H. C. Williams (1994)

Journal de théorie des nombres de Bordeaux

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It is well known that the continued fraction expansion of D readily displays the midpoint of the principal cycle of ideals, that is, the point halfway to a solution of x 2 - D y 2 = ± 1 . Here we notice that, analogously, the point halfway to a solution of x 2 - D y 2 = - 3 can be recognised. We explain what is going on.