Travelling Waves for Fourth Order Parabolic Equations
نویسندگان
چکیده
We study travelling wave solutions for a class of fourth order parabolic equations. Travelling wave fronts of the form u(x, t) = U(x + ct), connecting homogeneous states, are proven to exist in various cases: connections between two stable states, as well as connections between an unstable and a stable state, are considered.
منابع مشابه
Convergence to Travelling Waves in a Reaction-diffusion System Arising in Contaminant Transport
We consider a nonlinear system of parabolic equations describing the transport of contaminant in porous media. For this system travelling wave solutions are known to exist. We prove existence and uniqueness of general solutions of the system and convergence to travelling waves.
متن کاملA variational proof of global stability for bistable travelling waves
We give a variational proof of global stability for bistable travelling waves of scalar reaction-diffusion equations on the real line. In particular, we recover some of the classical results by P. Fife and J.B. McLeod (1977) without any use of the maximum principle. The method that is illustrated here in the simplest possible setting has been successfully applied to more general parabolic or hy...
متن کاملOn the Structure of Spectra of Modulated Travelling Waves
Modulated travelling waves are solutions to reaction–diffusion equations that are time–periodic in an appropriate moving coordinate frame. They may arise through Hopf bifurcations or essential instabilities from pulses or fronts. In this article, a framework for the stability analysis of such solutions is presented: the reaction–diffusion equation is cast as an ill–posed elliptic dynamical syst...
متن کاملOn the Structure of Spectra of Modulated Travelling Waves
Modulated travelling waves are solutions to reaction-diiusion equations that are time-periodic in an appropriate moving coordinate frame. They may arise through Hopf bifurcations or essential instabilities from pulses or fronts. In this article, a framework for the stability analysis of such solutions is presented. The issue is to cast the reaction-diiusion equation as an ill-posed dynamical sy...
متن کاملA simple mathematical model inspired by the Purkinje cells: from delayed travelling waves to fractional diffusion
Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Math. Analysis
دوره 32 شماره
صفحات -
تاریخ انتشار 2001