Existence and nonexistence of solutions for the heat equation with a superlinear source term
Existence and nonexistence of solutions for the heat equation with a superlinear source term
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DOI：
10.1016/j.matpur.2018.08.001
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发表时间：
2016-09
期刊：
影响因子：
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通讯作者：
Y. Fujishima;Norisuke Ioku
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文献类型：
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作者：
Y. Fujishima;Norisuke Ioku
本文建立了非线性热方程初值问题局部时间解的存在性和不存在性的分类理论。通过研究一类拟尺度性质及其不变积分，揭示了初值的阈值可积性，从而区分了解的存在性和不存在性。典型的非线性项，如多项式型、指数型及其和、积、合成等都可以作为应用。
We develop a classification theory for the existence and non-existence of local in time solutions for initial value problems for nonlinear heat equations. By focusing on some quasi-scaling property and its invariant integral, we reveal the explicit threshold integrability of initial data that classifies the existence and nonexistence of solutions. Typical nonlinear terms, for instance polynomial type, exponential type and their sums, products and compositions can be treated as applications.