<p style='text-indent:20px;'>In this paper, we are concerned with the existence of solitary waves for a generalized Kawahara equation, which is model equation describing solitary-wave propagation in media. We obtain some qualitative properties equilibrium points and results wave solutions without delay perturbation by employing phase space analysis. Furthermore two types special convoluti...

We consider the Kuramoto-Sivashinsky (KS) equation in finite domains of the form [−L,L]d. Our main result provides refined Gevrey estimates for the solutions of the one dimensional differentiated KS, which in turn imply effective new estimates for higher Sobolev norms of the solutions in terms of powers of L. We illustrate our method on a simpler model, namely the regularized Burger’s equation....

This paper deals with the null-controllability of a system mixed parabolic-elliptic pdes at any given time T>0. More precisely, we consider Kuramoto-Sivashinsky–Korteweg-de Vries equation coupled second order elliptic posed in interval (0,1). We first show that linearized is globally null-controllable by means localized interior control acting on either KS-KdV or equation. Using Carleman approa...

We are interested in solution techniques for backward–in–time evolutionary PDE problems arising in fluid mechanics. In addition to their intrinsic interest, such techniques have applications in the recently proposed retrograde data assimilation. As our model system we consider the terminal value problem for the Kuramoto–Sivashinsky equation in a 1D periodic domain. Such backward problems are ty...