We prove that the initial value problem (IVP) for the BBM equation is ill-posed for data in H(R), s < 0 in the sense that the flow-map u0 7→ u(t) that associates to initial data u0 the solution u cannot be continuous at the origin from H(R) to even D′(R) at any fixed t > 0 small enough. This result is sharp.

The anisotropic-diffusion convection equation of spatiallyvariable coefficients which is relevant for functionally graded mediais discussed in this paper to find numerical solutions by using acombined Laplace transform and boundary element method. variablecoefficients transformed a constant equation.The then Laplace-transformed sothat the time variable vanishes. equationis consequently written ...

The paper concerns capillary-gravity surface waves propagating on a two-dimensional incompressible and inviscid fluid with or without an obstacle placed at flat horizontal bottom. Formally second-order correct model equations, analogous to the first-order KdV equation, are derived under classical assumptions of long wavelength small amplitude waves. equations fifth-order type where bottom intro...

this article is devoted to study of the autoconvolution equations and generalized mittag-leffler functions. these types of equations are given in terms of the laplace transform convolution of a function with itself. we state new classes of the autoconvolution equations of the first kind and show that the generalized mittag-leffler functions are solutions of these types of equations. in view of ...

In this paper, a simple, robust, fast and effective method based on the conserved quantities is developed to approximate analyse shape, structure interaction characters of solitary waves described by Benjamin–Bona–Mahony (BBM) equation. Due invariant character quantities, there no need solve related complex nonlinear partial differential BBM equation simulate interactions between at most mergin...

Dietary proteins are recognized by the gastrointestinal tract to display physiological functions, however, the sensory mechanism of the intestinal mucosa is not known. We examined binding properties between the rat small intestinal brush-border membrane (BBM) and proteins by using a surface plasmon resonance biosensor. BBM and solubilized BBM prepared from the rat jejunum bound to casein immobi...