The purpose of this course is to study the dynamics of PDE on thin domains. The main
motivation of this kind of problems comes from two sources. The first source is physics; thin …

One of the major problems in the study of evolution equations of mathematical physics is the
investigation of the behavior of the solutions to these equations when time is large or tends …

The main goal of this paper is to obtain the exact solutions of the stochastic real-valued
Ginzburg–Landau equation, which is forced by multiplicative noise in the Itô sense. It is …

In this manuscript, the improved modified extended tanh integration technique is
implemented to investigate the exact solutions of stochastic Ginzburg–Landau model driven …

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We evaluate several alternative methods for the approximation of inertial manifolds for the
one-dimensional Kuramoto-Sivashinsky equation (KSE). A method motivated by the …

This survey is devoted to an introduction to the theory of global attractors for semigroups
defined on infinite dimensional spaces, which has mainly been developed in the last three …

Surveying both theoretical and experimental aspects of chaotic behavior, this book presents
chaos as a model for many seemingly random processes in nature. Basic notions from the …

The authors present a connection between the concepts of determining nodes and inertial
manifolds with that of finite difference and finite volumes approximations to dissipative partial …

An inertial manifold is constructed for the scalar reaction-diffusion equation ut= vu xx+ ƒ (u)
with a cubic nonlinearity. Uniform bounds are obtained for the number of zeros along …