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• W2086393698 abstract "We consider the semilinear heat equation ut = Δu + up both in ℝN and in a bounded domain with homogeneous Dirichlet boundary conditions, with 1 T, we consider a natural approximation by reaction problems with global solution and pass to the limit. As is well-known, the limit solution undergoes complete blowup: after it blows up at t = T, the continuation is identically infinite for all t > T.We perform here a deeper analysis of how complete blowup occurs. Actually, the singularity set of a solution that blows up as t ↗ T propagates instantaneously at time t = T to cover the whole space, producing a catastrophic discontinuity between t = T− and t = T+. This is called the “avalanche.” We describe its formation as a layer appearing in the limit of the natural approximate problems. After a suitable scaling, the initial structure of the layer is given by the solution of a limit problem, described by a simple ordinary differential equation. As t proceeds past T, the solutions of the approximate problems have a traveling wave behavior with a speed that we compute. The situation in the inner region depends on the type of approximation: a conical pattern is formed with time when we approximate the power up by a flat truncation at level n, while for tangent truncations we get an exponential increase in time and a diffusive spatial pattern. © 2003 Wiley Periodicals, Inc." @default.
• W2086393698 created "2016-06-24" @default.
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• W2086393698 date "2003-10-21" @default.
• W2086393698 modified "2023-09-24" @default.
• W2086393698 title "Thermal avalanche for blowup solutions of semilinear heat equations" @default.
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• W2086393698 doi "https://doi.org/10.1002/cpa.10112" @default.
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