Galerkin-Ritz procedures for approximate solutions to systems of reaction-diffusion equations |
| |
Authors: | Gerald Rosen |
| |
Institution: | (1) Drexel University, 19104 Philadelphia, Pennsylvania, U.S.A. |
| |
Abstract: | For any essentially nonlinear system of reaction-diffusion equations of the generic form ∂ci/∂t=Di∇2ci+Qi(c,x,t) supplemented with Robin type boundary conditions over the surface of a closed bounded three-dimensional region, it
is demonstrated that all solutions for the concentration distributionn-tuple function c=(c
1(x,t),...,c
n
(x,t)) satisfy a differential variational condition. Approximate solutions to the reaction-diffusion intial-value boundary-value
problem are obtainable by employing this variational condition in conjunction with a Galerkin-Ritz procedure. It is shown
that the dynamical evolution from a prescribed initial concentrationn-tuple function to a final steady-state solution can be determined to desired accuracy by such an approximation method. The
variational condition also admits a systematic Galerkin-Ritz procedure for obtaining approximate solutions to the multi-equation
elliptic boundary-value problem for steady-state distributions c=−c(x). Other systems of phenomenological (non-Lagrangian)
field equations can be treated by Galerkin-Ritz procedures based on analogues of the differential variational condition presented
here. The method is applied to derive approximate nonconstant steady-state solutions for ann-species symbiosis model. |
| |
Keywords: | |
本文献已被 ScienceDirect SpringerLink 等数据库收录! |
|