Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On a second-order boundary value problem arising in combustion theory

Author: Philip Holmes
Journal: Quart. Appl. Math. 40 (1982), 53-62
MSC: Primary 34B15; Secondary 80A25
DOI: https://doi.org/10.1090/qam/652049
MathSciNet review: 652049
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Abstract: We obtain existence and uniqueness results for the boundary-value problem

$\displaystyle y'' = {x^2} - {y^2}, \qquad y\left( x \right) \sim \mp x \qquad as \qquad x \to \pm \infty $

. Our main result shows that there are precisely two solutions $ {y_+} \left( x \right) > - \left\vert x \right\vert$ and $ {y_-}\left( x \right) < - \left\vert x \right\vert$. Only the latter is of physical interest in the problem in combustion theory from which the equation arises.

References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/652049
Article copyright: © Copyright 1982 American Mathematical Society

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