A Note on the Solution of Reaction-diffusion Equations with Convection Export

@article{Lee_IMAJApplMath82, abstract = {Two coupled linear reaction-diffusion equations with convection terms are considered. These equations contain eight arbitrary real constants (four reaction rates, two diffusivities and two convection constants) and therefore encompass a wide variety of differing physical situations. Boundary value problems for this system are of course amenable to classical transform techniques; however, the technical difficulties encountered are, in general, overwhelming. In a previous article (Hill, 1981) appearing in this journal, explicit solutions of a general nature are given for the system without the convection terms. Here, by an indirect approach the source solutions are developed and subsequently more general solutions for the reaction-diffusion system with convection. These general results are not as useful for boundary value problems as their counterparts for the system without the convection terms. However, some insight into the underlying structure of the equations is revealed as well as providing formulae for solutions which demonstrate the explicit dependence on the eight parameters of the system. Asymptotic source solutions are noted for small and large times. 10.1093/imamat/29.1.39}, author = {Lee, Alexander I. and Hill, James M.}, citeulike-article-id = {6112045}, citeulike-linkout-0 = {http://dx.doi.org/10.1093/imamat/29.1.39}, citeulike-linkout-1 = {http://imamat.oxfordjournals.org/content/29/1/39.abstract}, citeulike-linkout-2 = {http://imamat.oxfordjournals.org/content/29/1/39.full.pdf}, day = {1}, doi = {10.1093/imamat/29.1.39}, journal = {IMA J Appl Math}, keywords = {mathematics, pde, reaction-diffusion, theory}, month = {July}, number = {1}, pages = {39--43}, posted-at = {2009-11-14 20:24:21}, priority = {2}, title = {A Note on the Solution of Reaction-diffusion Equations with Convection}, url = {http://dx.doi.org/10.1093/imamat/29.1.39}, volume = {29}, year = {1982} }

TY - JOUR ID - Lee_IMAJApplMath82 L3 - citeulike-article-id:6112045 N2 - Two coupled linear reaction-diffusion equations with convection terms are considered. These equations contain eight arbitrary real constants (four reaction rates, two diffusivities and two convection constants) and therefore encompass a wide variety of differing physical situations. Boundary value problems for this system are of course amenable to classical transform techniques; however, the technical difficulties encountered are, in general, overwhelming. In a previous article (Hill, 1981) appearing in this journal, explicit solutions of a general nature are given for the system without the convection terms. Here, by an indirect approach the source solutions are developed and subsequently more general solutions for the reaction-diffusion system with convection. These general results are not as useful for boundary value problems as their counterparts for the system without the convection terms. However, some insight into the underlying structure of the equations is revealed as well as providing formulae for solutions which demonstrate the explicit dependence on the eight parameters of the system. Asymptotic source solutions are noted for small and large times. 10.1093/imamat/29.1.39 IS - 1 JF - IMA J Appl Math EP - 43 TI - A Note on the Solution of Reaction-diffusion Equations with Convection VL - 29 SP - 39 KW - mathematics KW - pde KW - reaction-diffusion KW - theory AU - Lee, Alexander AU - Hill, James PY - 1982/07/01/ UR - http://dx.doi.org/10.1093/imamat/29.1.39 ER -