论文信息 - Blow up of solutions to the second sound equation in one space dimension

Blow up of solutions to the second sound equation in one space dimension

In this paper, we study blow ups of solutions to the second sound equation ∂2 t u= u∂x(u∂xu), which is more natural than the second sound equation in Landau–Lifshitz’s text in large time. We assume that the initial data satisfies u(0, x)≥ δ > 0 for some δ. We give sufficient conditions that two types of blow up occur: one of the two types is that L∞-norm of ∂tu or ∂xu goes up to the infinity; the other type is that u vanishes, that is, the equation degenerates.

Keiichi Kato | Yuusuke Sugiyama

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