We investigate the solutions of the nonlinear heat equation with a volume heat source and thermal conductivity dependent on a negative power of temperature. Properties of self-similar solutions are examined. Structures with contracting half-width evolve in the LS-regime with blowup. Self-similar analysis shows that the system attains a self-similar regime. The nonlinear heat equation is applied to model fast heating of the plasma in flares forming in a magnetic tube cross section, when heat is propagated by plasma ions across the magnetic field. Microflares are described by localized structures evolving in LS-regime with blowup. They may form thin hot filaments stretched in the direction of the magnetic field. The modeling results are consistent with experimental observations.
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Translated from Prikladnaya Matematika i Informatika, No. 50, 2015, pp. 5–30.
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Kurkina, E.S., Troshchiev, Y.V., Kovalev, V.A. et al. Small-Scale Heat Localization with Blowup in the Magnetic-Tube Cross Section During a Solar Flare. Comput Math Model 27, 395–416 (2016). https://doi.org/10.1007/s10598-016-9330-5
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DOI: https://doi.org/10.1007/s10598-016-9330-5