化学反応論に現れる半線型楕円型境界値問題の研究

概要

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This paper is devoted to the study of a semilinear elliptic boundary value problem arising in chemical reactor theory which obeys the simple Arrhenius rate law and Newtonian cooling. We prove that if the activation energy is low then only a smooth progression of reaction rate with imposed ambient temperature can occur, and prove that if the activation energy is sufficiently large then ignition and extinction phenomena occur in the stable steady temperature profile at some critical values of a dimensionless heat evolution rate, more precisely, in the latter case we show that the semilinear problem with a positive parameter related to the heat evolution rate, has at least three positive solutions in some open interval of the parameter and has a unique positive solution for any value of the parameter which is sufficiently large or small. Moreover the asymptotic behavior and stability of the stable steady temperature are also studied.
前橋工科大学の論文
1998-04-09