Multiple layered solutions of the nonlocal bistable equation
نویسندگان
چکیده
منابع مشابه
Multiple Layered Solutions of the Nonlocal Bistable Equation
The nonlocal bistable equation is a model proposed recently to study materials whose constitutive relations among the variables that describe their states are nonlocal. It resembles the local bistable equation (the Allen-Cahn equation) in some way, but contains a much richer set of solutions. In this paper we consider two types of solutions. The first are the periodic solutions on a finite inte...
متن کاملThe nonlocal bistable equation : Stationary solutions on a bounded interval ∗
We discuss instability and existence issues for the nonlocal bistable equation. This model arises as the Euler-Lagrange equation of a nonlocal, van der Waals type functional. Taking the viewpoint of the calculus of variations, we prove that for a class of nonlocalities this functional does not admit nonconstant C local minimizers. By taking variations along nonsmooth paths, we give examples of ...
متن کاملUnbounded solutions of the nonlocal heat equation
We consider the Cauchy problem posed in the whole space for the following nonlocal heat equation: ut = J ∗u−u , where J is a symmetric continuous probability density. Depending on the tail of J , we give a rather complete picture of the problem in optimal classes of data by: (i) estimating the initial trace of (possibly unbounded) solutions; (ii) showing existence and uniqueness results in a su...
متن کاملPulses and waves for a bistable nonlocal reaction-diffusion equation
A bistable nonlocal reaction-diffusion equation is studied. Solutions in the form of simple and periodic travelling waves, single and multiple pulses are observed in numerical simulations. Successive transitions from simple waves to periodic waves and to stable pulses are described.
متن کاملAsymptotic solutions of the 1D nonlocal Fisher-KPP equation
Two analytical methods have been developed for constructing approximate solutions to a nonlocal generalization of the 1D Fisher– Kolmogorov–Petrovskii–Piskunov equation. This equation is of special interest in studying the pattern formation in microbiological populations. In the greater part of the paper, we consider in detail a semiclassical approximation method based on the WKB–Maslov theory ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 2000
ISSN: 0167-2789
DOI: 10.1016/s0167-2789(00)00143-3