Nonlocal gravity and the diffusion equation
نویسندگان
چکیده
منابع مشابه
A Nonlocal Convection-diffusion Equation
In this paper we study a nonlocal equation that takes into account convective and diffusive effects, ut = J ∗u−u+G ∗ (f(u))− f(u) in R, with J radially symmetric and G not necessarily symmetric. First, we prove existence, uniqueness and continuous dependence with respect to the initial condition of solutions. This problem is the nonlocal analogous to the usual local convection-diffusion equatio...
متن کاملA Logistic Equation with Refuge and Nonlocal Diffusion
In this work we consider the nonlocal stationary nonlinear problem (J ∗ u)(x) − u(x) = −λu(x) + a(x)u(x) in a domain Ω, with the Dirichlet boundary condition u = 0 in R \ Ω and p > 1. The kernel J involved in the convolution (J ∗ u)(x) = RN J(x− y)u(y) dy is a smooth, compactly supported nonnegative function with unit integral, while the weight a(x) is assumed to be nonnegative and is allowed t...
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 Behaviour for a Nonlocal Diffusion Equation on a Lattice
In this paper we study the asymptotic behaviour as t → ∞ of solutions to a nonlocal diffusion problem on a lattice, namely, un(t) = P j∈Zd Jn−juj(t)− un(t) with t ≥ 0 and n ∈ Z. We assume that J is nonnegative and verifies Pn∈Zd Jn = 1. We find that solutions decay to zero as t → ∞ and prove an optimal decay rate using, as our main tool, the discrete Fourier transform.
متن کاملBlowup Analysis for a Nonlocal Reaction Diffusion Equation with Potential
In this paper we investigate a nonlocal reaction diffusion equation with potential, under Neumann boundary. We obtain the complete classification of the parameters for which the solution blows up in finite time or exists globally. Moreover, we study the blowup rate and the blowup set for the blowup solution. Key–Words: Nonlocal diffusion, Blow up, Blowup rate, Blowup set
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: Physical Review D
سال: 2010
ISSN: 1550-7998,1550-2368
DOI: 10.1103/physrevd.82.123518