Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



A mathematical model of solar flares

Authors: Jean Heyvaerts, Jean-Michel Lasry, Michelle Schatzman and Patrick Witomski
Journal: Quart. Appl. Math. 41 (1983), 1-30
MSC: Primary 85A30; Secondary 58E99
DOI: https://doi.org/10.1090/qam/700658
MathSciNet review: 700658
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Abstract: The phenomenon of solar flares is modeled assuming that the magnetic field is force-free and that its evolution is quasi-static. This model is simplified so as to be tractable and yields a semi-linear elliptic equation in a halfplane depending on a parameter $ \lambda $ which describes the time evolution. It is proved that there are (at least) two branches of solutions which have distinct asymptotic behaviors at infinity. The upper branch exists for all $ \lambda > 0$, but the lower branch exists only on a finite interval $ \left[ {0,{\lambda ^c}} \right]$. As stable solutions must have the same asymptotic behavior as the lower branch of solutions, and as this is impossible after $ {\lambda ^c}$, we contend that no stable solution exists after $ {\lambda ^c}$ and that a solar flare is thus triggered.

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DOI: https://doi.org/10.1090/qam/700658
Article copyright: © Copyright 1983 American Mathematical Society

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