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MR1802001 35R35 (35B35 35K55 35K57)
Ghidouche, Hamid; Souplet, Philippe; Tarzia, Domingo Decay of global solutions, stability and blowup for a reaction-diffusion problem with free boundary. Proc. Amer. Math. Soc. 129 (2001), no. 3, 781–792.
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