We establish some general theorems for the existence and nonexistence of ground state
solutions of steady-state N coupled nonlinear Schrödinger equations. The sign of coupling …

Dissipative equations have attracted substantial attention over many years. Much progress
has been achieved in this area using a combination of both finite dimensional and infinite …

We develop a conservative, second-order accurate fully implicit discretization of the Navier–
Stokes (NS) and Cahn–Hilliard (CH) system that has an associated discrete energy …

We consider the problem, where Ω is a bounded smooth domain in RN, ɛ> 0 is a small
parameter, and ƒ is a superlinear, subcritical nonlinearity. It is known that this equation …

Models for phase separation and their mathematics Page 1 Electronic Journal of Differential
Equations, Vol. 2000(2000), No. 48, pp. 1–26. ISSN: 1072-6691. URL: http://ejde.math.swt.edu …

Equations for a material that can exist stably in one of two homogeneous states are derived
from a microscopic or lattice viewpoint with the assumption that the evolution follows a …

Here we study the interaction and the configuration of spikes in a double condensate by
analyzing least energy solutions of two coupled nonlinear Schrödinger equations which …

We study the interior spike solutions to a steady state problem of the shadow system of the
Gierer–Meinhardt system arising from biological pattern formation. We first show that at a …

In this paper, we study mathematical properties of an integro-differential equation that arises
as a particular limit case in the study of individual cell-based model. We obtain global well …

We study the existence, uniqueness and continuous dependence on initial data of the
solution to a nonlocal Cahn–Hilliard equation on a bounded domain. The equation …