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• W1569477826 abstract "We consider a one-phase Stefan problem for the heat equation with a nonlinear reaction term. We first exhibit an energy condition, involving the initial data, under which the solution blows up in finite time in $L^infty$ norm. We next prove that all global solutions are bounded and decay uniformly to 0, and that either: (i) the free boundary converges to a finite limit and the solution decays at an exponential rate, or (ii) the free boundary grows up to infinity and the decay rate is at most polynomial. Finally, we show that small data solutions behave like (i)." @default.
• W1569477826 created "2016-06-24" @default.
• W1569477826 creator A5087982446 @default.
• W1569477826 date "2000-09-20" @default.
• W1569477826 modified "2023-10-17" @default.
• W1569477826 title "Decay of global solutions, stability and blowup for a reaction-diffusion problem with free boundary" @default.
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• W1569477826 doi "https://doi.org/10.1090/s0002-9939-00-05705-1" @default.
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