It is well known that the existence of traveling wave solutions (TWS) for many partial differential equations (PDE) a consequence fact an associated planar ordinary equation (ODE) has certain types defined all time. In this paper we address problem persistence TWS given PDE under small perturbations. Our main results deal with situation where ODE center and, as consequence, original continuum p...

Hocherman and Rosenau conjectured that long-wave unstable Cahn-Hilliard-type interface models develop finite-time singularities when the nonlinearity in the destabilizing term grows faster at large amplitudes than the nonlinearity in the stabilizing term (Phys. D 67, 1993, pp. 113–125). We consider this conjecture for a class of equations, often used to model thin films in a lubrication context...

In this article, we design a novel linearized and momentum-preserving Fourier pseudo-spectral scheme to solve the Rosenau-Korteweg de Vries equation. With aid of new semi-norm equivalence between method finite difference method, prior bound numerical solution in discrete L ∞ $$ {L}^{\infty } -norm is obtained from momentum conservation law. Subsequently, based on energy solution, show that, wit...

This paper is devoted to hyperbolic systems of balance laws with non local source terms. The existence, uniqueness and Lipschitz dependence proved here comprise previous results in the literature and can be applied to physical models, such as Euler system for a radiating gas and Rosenau regularization of the Chapman-Enskog expansion. 2000 Mathematics Subject Classification: 35L65, 76N15