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Nonlocal reaction—diffusion equations and nucleation

IMA Journal of Applied Mathematics, 1992
Summary: A nonlocal reaction-diffusion equation is presented and analysed using matched asymptotic expansions and multiple timescales. The problem models a binary mixture undergoing phase separation. The particular form of the equation is motivated by arguments from the calculus of variations, with the nonlocality arising from an enforcement of ...
Rubinstein, Jacob, Sternberg, Peter
openaire   +1 more source

Modified Douglas splitting methods for reaction–diffusion equations

BIT Numerical Mathematics, 2015
We present modifications of the second-order Douglas stabilizing corrections method, which is a splitting method based on the implicit trapezoidal rule.
Andrés Arrarás, K. J. I. '. Hout, W. Hundsdorfer, L. Portero   +3 more
semanticscholar   +1 more source

Adaptive FEM for reaction—diffusion equations

Applied Numerical Mathematics, 1998
In the first part of the paper the author shortly presents some methods for solving mixed systems of nonlinear parabolic and elliptic differential equations. Especially a short comparison between the adaptive method of lines and Rothe's approach is presented. Then the author describes the time integrator and the finite element method (FEM) derived from
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Nonlocal Reaction-diffusion Equations

2014
We introduced nonlocal reaction-diffusion equations in Section 2.4 of Chapter 1 by means of the model of competition of species. It is also possible to view them in a different way. If individuals of some population consume resources in some area around their average position, then we need to take into account this nonlocal consumption of resources in ...
openaire   +1 more source

Exact Solutions of Reaction-Diffusion Equation

Journal of the Physical Society of Japan, 1993
Summary: The statitical interactions of anyons on a plane are described by a gauge field. We present a natural periodic generalization of such gauge field and find that this agrees with the corresponding gauge field on a torus which has been obtained from the Chern-Simons theory.
openaire   +2 more sources

Fast-Diffusion Limit for Reaction–Diffusion Equations with Degenerate Multiplicative and Additive Noise

Journal of Dynamics and Differential Equations, 2020
W. Mohammed
semanticscholar   +1 more source

Reaction - diffusion equations in perforated media

Nonlinearity, 1997
The author considers the problem \[ {\partial\over\partial t} u(t,x)= {1\over 2} \sum^r_{i,j= 1} a_{ij}(x){\partial^2\over \partial x_i\partial x_j} u(t,x)+ \sum^r_{i= 1} b_i(x){\partial\over\partial x_i} u(t,x),\;t\in (0,\infty),\;x\in D= \mathbb{R}^r\setminus \bigcup^\infty_{i= 1} H_i, \] \[ {\partial u\over\partial n}+ f(x,u)= 0,\;x\in\bigcup ...
openaire   +2 more sources

Reaction–diffusion Equations

Leonardo Dagdug, Jason Peña, Ivan Pompa-García   +2 more
  +4 more sources

Numerical simulation of fractional-order reaction–diffusion equations with the Riesz and Caputo derivatives

Neural computing & applications (Print), 2019
K. Owolabi
semanticscholar   +1 more source

Spreading Speeds for Reaction–Diffusion Equations with a Shifting Habitat

Journal of Dynamics and Differential Equations, 2019
Changbing Hu, Jin Shang, Bingtuan Li
semanticscholar   +1 more source