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arXiv · 1911.01844

The Blow-up solutions for fractional heat equations on torus and Euclidean space

Divyang G. Bhimani
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Abstract

We produce a finite time blow-up solution for nonlinear fractional heat equation ($\partial_t u + (-\Delta)^{\beta/2}u=u^k$) in modulation and Fourier amalgam spaces on the torus $\mathbb T^d$ and the Euclidean space $\mathbb R^d.$ This complements several known local and small data global well-posedness results in modulation spaces on $\mathbb R^d.$ Our method of proof rely on the formal solution of the equation. This method should be further applied to other non-linear evolution equations.

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Divyang G. Bhimani. 2019-11-03. The Blow-up solutions for fractional heat equations on torus and Euclidean space. https://arxiv.org/abs/1911.01844

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