An Invariance Principle for Random Traveling Waves in One Dimension
نویسنده
چکیده
We consider solutions to a nonlinear reaction diffusion equation when the reaction term varies randomly with respect to the spatial coordinate. The nonlinearity is either the ignition nonlinearity or the bistable nonlinearity, under suitable restrictions on the size of the spatial fluctuations. It is known that the solution develops an interface which propagates with a well-defined speed in the large-time limit. The main result of this article is a functional central limit theorem for the random interface position.
منابع مشابه
Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves
The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...
متن کاملA Quenched Invariance Principle for Certain Ballistic Random Walks in I.i.d. Environments
ABSTRACT. We prove that every nearest neighbor random walk in i.i.d. environment in dimension greater than or equal to 4 that has an almost sure positive speed in a certain direction, an annealed invariance principle and some mild integrability condition for regeneration times also satisfies a quenched invariance principle. The argument is based on intersection estimates and a theorem of Boltha...
متن کاملAn Invariance Principle for Brownian Motion in Random Scenery
We prove an invariance principle for Brownian motion in Gaussian or Poissonian random scenery by the method of characteristic functions. Annealed asymptotic limits are derived in all dimensions, with a focus on the case of dimension d = 2, which is the main new contribution of the paper.
متن کامل1 Mind and Brain : A Catalytic Theory of Embodiment
This paper describes a catalytic theory that grounds cognition in biology. An enzyme is a biological catalyst that increases the speed of a molecular reaction; the reaction is thought to occur via a traveling wave, a soliton, whose formation and persistence depend on the structure or invariance of the catalytic environment. Generalizing to cognition, the invariance of perceptual events plays th...
متن کاملTraveling waves for the Nonlinear Schrödinger Equation with general nonlinearity in dimension one
We study the traveling waves of the Nonlinear Schrödinger Equation in dimension one. Through various model cases, we show that for nonlinearities having the same qualitative behaviour as the standard Gross-Pitaevkii one, the traveling waves may have rather different properties. In particular, our examples exhibit multiplicity or nonexistence results, cusps (as for the Jones-Roberts curve in the...
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 43 شماره
صفحات -
تاریخ انتشار 2011