This paper considers the initial value problem for nonlinear heat equation in the whole space \(\mathbb{R}^{N}\). The local existence theory related to the finite time blow-up is also obtained for the problem with nonlinearity source (like polynomial types).

中文翻译：

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一类半线性热方程的适定性结果和爆破

本文考虑了整个空间\（\ mathbb {R} ^ {N} \）中非线性热方程的初值问题。对于具有非线性源（如多项式类型）的问题，还获得了与有限时间爆炸有关的局部存在理论。