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Existence for the modified Kassoy problem

Published online by Cambridge University Press:  14 November 2011

J. Bebernes  and
W. Troy
J. Bebernes
Affiliation:
Department of Mathematics, University of Colorado, Campus Box 426, Boulder, Colorado 80309, U.S.A.
W. Troy
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.
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Synopsis

We prove that there exists an ᾱ > 0 such that for each 0 ≦ α ≦ ᾱ, there is at least one β = β(α) < 0 such that y“ − (x/2)y' + ey − 1 =0, y(0) = α, y'(0) = β has a solution y(x, α,β) satisfying the asymptotic property y(x, α,β)∼ −2 In x + Kα as x → ∞.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 1-2 , 1987 , pp. 131 - 136
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Bebernes, J. and Troy, W.. Nonexistence for the Kassoy problem. SIAM J. Math. Anal, (to appear).Google Scholar
2Bebernes, J. and Kassoy, D.. A mathematical analysis of blowup for thermal reactions—the spatially nonhomogeneous case. SIAM J. Appl. Math. 40 (1981), 476–484.Google Scholar
3Dold, J. W.. Analysis of the early stage of thermal runaway. Quart. J. Mech. Appl. Math. 38 (1985), 361–387.CrossRefGoogle Scholar
4Friedman, A. and McLeod, B.. Blow-up of positive solutions of semilinear heat equations. Indiana Univ. Math. J. 34 (1985), 425–447.CrossRefGoogle Scholar
5Kapila, A. K.. Reactive-diffusive system with Arrhenius kinetics: Dynamics of ignition. SIAM J. Appl. Math. 39 (1980), 21–36.CrossRefGoogle Scholar
6Kassoy, D. R. and Poland, J.. The thermal explosion confined by a constant temperature boundary: I. The induction period solution. SIAM J. Appl. Math. 39 (1980), 412–430.CrossRefGoogle Scholar
7Kassoy, D. R. and Poland, J.. The thermal explosion confined by a constant temperature boundary: II. The extremely rapid transient. SIAM J. Appl. Math. 41 (1981), 231–246.Google Scholar
8Lacey, A. A.. Mathematical analysis of thermal runaway for spatially inhomogeneous reactions. SIAMJ. Appl. Math. 43 (1983), 1350–1366.CrossRefGoogle Scholar
9Lacey, A. A.. The form of blowup for nonlinear parabolic equations. Proc. Roy. Soc. Edinburgh Sect. A 98 (1984), 183–202.Google Scholar