the assumptions considered in developing the saint-venant equations limit their application in many practical situations. the modified boussinesq equation was presented to overcome the limitation imposed by saint-venant equation due to the presence of non-hydrostatic pressure distribution and steep slope. in this paper a computational model was developed for solving the modified and the traditi...

s of IWANASP, October 22 – 24, 2015, Lagos, Portugal A FAST FOURIER–GALERKIN METHOD SOLVING A BOUNDARY INTEGRAL EQUATION FOR THE BIHARMONIC EQUATION

The stability of the functional equation f(x composite function y) = H(f(x), f(y)) (x, y in S) is investigated, where H is a homogeneous function and composite function is a square-symmetric operation on the set S. The results presented include and generalize the classical theorem of Hyers obtained in 1941 on the stability of the Cauchy functional equation.

We study the interaction of suitable small and high frequency waves evolving by the flow of the Benjamin-Ono equation. As a consequence, we prove that the flow map of the Benjamin-Ono equation can not be uniformly continuous on bounded sets of H s (R) for s > 0.

We establish some decay properties of the semigroup generated by a linear integro-differential equation in a Hilbert space, which is an abstract version of the equation ut(t)− β∆u(t)− ∫ ∞ 0 k(s)∆u(t− s)ds = 0 describing hereditary heat conduction.

This paper is concerned with the Cauchy problem of the modified Kawahara equation. By using the Fourier restriction norm method introduced by Bourgain, and using the I-method as well as the L 2 conservation law, we prove that the modified Kawahara equation is globally well-posed for the initial data in the Sobolev space H s (R) with s > − 3 22 .