# ON exact dead-core rates for a semilinear heat equation with strong absorption

Yukihiro Seki

11 被引用数 (Scopus)

## 抄録

We study a semilinear heat equation with strong absorption ut = u - up with 0 < p < 1 in RN. A solution is known to develop dead-core in finite time for a wide class of initial data. We construct specific solutions with exact dead-core rates faster than the one given by the corresponding ODE. They are constructed formally by means of matched asymptotic expansion technique and rigorously by means of topological fixed-point arguments based on a priori estimates. To obtain the a priori estimates, we analyze a certain linearized problem in a new function space $\mathcal{H}'$.

本文言語 英語 1-52 52 Communications in Contemporary Mathematics 13 1 https://doi.org/10.1142/S0219199711004154 出版済み - 2 2011 はい

• 数学 (全般)
• 応用数学

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