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Unbounded solutions of the nonlocal heat equation

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URI: https://hdl.handle.net/10016/22186
ISSN: 1534-0392
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2011-11
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American Institute of Mathematical Sciences
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We consider the Cauchy problem posed in the whole space for the following nonlocal heat equation: where is a symmetric continuous probability density. Depending on the tail of , we give a rather complete picture of the problem in optimal classes of data by: estimating the initial trace of (possibly unbounded) solutions; showing existence and uniqueness results in a suitable class; proving blow-up in finite time in the case of some critical growths; giving explicit unbounded polynomial solutions.
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Matemáticas, Matemáticas aplicadas
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