A mathematical analysis of thermal explosions

Taira, Kazuaki

doi:10.1155/s0161171201006706

Cited by 2 publications

(1 citation statement)

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“…Wang [33] and Du [15] discussed in great detail the isothermal case (Dirichlet case) under general Arrhenius reaction rate laws (see Remark 2.2 below). The present paper is devoted to the study of the existence of positive solutions of the problem (1.1), and is an expanded and revised version of the previous works Taira-Umezu [31] and Taira [27] and [28].…”

Section: Statement Of Main Resultsmentioning

confidence: 99%

Bifurcation curves in a combustion problem with general Arrhenius reaction-rate laws

Taira

2016

Ann Univ Ferrara

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This paper is devoted to the study of semilinear degenerate elliptic boundary value problems arising in combustion theory that obey a general Arrhenius equation and a general Newton law of heat exchange. Our degenerate boundary conditions include as particular cases the isothermal condition (Dirichlet condition) and the adiabatic condition (Neumann condition). We prove that ignition and extinction phenomena occur in the stable steady temperature profile at some critical values of a dimensionless rate of heat production. More precisely, we give sufficient conditions for our semilinear boundary value problems to have three positive solutions, which suggests that the bifurcation curves are S-shaped. Keywords Semilinear elliptic boundary value problem • Arrhenius equation • Newtonian cooling • ignition • extinction Mathematics Subject Classification (2010) 35J65 • 80A25

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