In this work, we consider the forced generalized Burgers-Huxley equation and establish the
existence and uniqueness of a global weak solution using a Faedo-Galerkin approximation …

The main goal of this paper is to classify the first transitions of a class of 1D second order
reaction diffusion equation with a non-self-adjoint linear part and semilinear nonlinearity on …

This article proposes a new approach for the design of low-dimensional suboptimal
controllers to optimal control problems of nonlinear partial differential equations (PDEs) of …

In this article, we study the dynamic transition for the one dimensional generalized Burgers
equation with periodic boundary condition. The types of transition are dictated by the sign of …

The 1D Burger's equation with Dirichlet boundary conditions exhibits a first transition from
the trivial steady state to a sinusoidal patterned steady state as the parameter λ which …

In this paper we study the dynamic bifurcation of the Swift-Hohenberg equation on a periodic
cell Ω=[− L, L]. It is shown that the equations bifurcates from the trivial solution to an attractor …

The goal of this article is to propose an efficient way of empirically improving suboptimal
solutions designed from the recent method of finite-horizon parameterizing manifolds (PMs) …

A general approach to provide approximate parameterizations of the" small" scales by the"
large" ones, is developed for stochastic partial differential equations driven by linear …

In this paper, we study dynamical Bifurcation of the Burgers-Fisher equation. We show that
the equation bifurcates an invariant set $\mathcal {A} _n (\beta) $ as the control parameter …

With his famous painting “The Treachery of Images” as duplicated in the previous page,
René Magritte coined in an essential way the fact that as realistic as possible a …