Blow-up solutions of fractional diffusion equations with an exponential nonlinearity

Nguyen, Anh; Caraballo, Tómas; Tuan, Nguyen

doi:10.1090/proc/16962

Blow-up solutions of fractional diffusion equations with an exponential nonlinearity
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by Anh Tuan Nguyen, Tómas Caraballo and Nguyen Huy Tuan;

Proc. Amer. Math. Soc. 152 (2024), 5175-5189

DOI: https://doi.org/10.1090/proc/16962

Published electronically: October 17, 2024

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Abstract:

The goal of this work is to investigate finite-time blow-up solutions to a class of time-space fractional diffusion equations with nonlinear exponential source terms. In contrast to the small critical data case, which leads to global solutions, we prove in this study that if the initial Schwartz data is large enough, our solutions will blow up in a finite time. The main idea of the analysis is based on the Fourier analytic approach and embeddings between Triebel-Lizorkin spaces and Besov spaces.

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Proceedings of the American Mathematical Society

Blow-up solutions of fractional diffusion equations with an exponential nonlinearity
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Abstract: