Semilinear Parabolic Boundary Value Problems in Combustion Theory

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J. Math. Sci. Univ. Tokyo
Vol. 10 (2003), No. 3, Page 455--494.

Taira, Kazuaki
Semilinear Parabolic Boundary Value Problems in Combustion Theory
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
This paper is devoted to the analytic semigroup approach to semilinear parabolic initial boundary value problems arising in combustion theory which obey a general Arrhenius equation and Newtonian cooling. We prove a global existence and uniqueness theorem of positive solutions by using the theory of analytic semigroups in the topology of uniform convergence. Moreover, we study the asymptotic stability of maximal and minimal positive solutions when there are multiple steady-state solutions.

Keywords: Semilinear parabolic boundary value problem, Arrhenius equation, Newtonian cooling, thermal explosion, analytic semigroup

Mathematics Subject Classification (1991): 35K60, 80A25

Mathematical Reviews Number: MR2002474

Received: 2002-06-14

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