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Life span bounds for reaction–diffusion equation with a space–time integral source term

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Abstract

In this paper, we study the blow-up phenomena of the Dirichlet initial boundary value problem for reaction–diffusion equation with a space–time integral source term. By virtue of Kaplan’s technique and some new properties on the system of differential inequalities, the method of constructing blow-up sub-solutions, we establish sufficient conditions to guarantee the solution blows up in finite time and give the upper bounds of life span. Moreover, based on constructing blow-up super-solutions and combining the auxiliary function method with the modified differential inequality techniques, lower bounds of life span are derived.

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Acknowledgements

The authors would like to deeply thank all the reviewers for their insightful and constructive comments.

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  1. School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, China

    Wentao Huo & Zhong Bo Fang

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  1. Wentao Huo
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Correspondence to Zhong Bo Fang.

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This work was supported by the Natural Science Foundation of Shandong Province of China (No. ZR2019MA072).

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Huo, W., Fang, Z.B. Life span bounds for reaction–diffusion equation with a space–time integral source term. Z. Angew. Math. Phys. 74, 128 (2023). https://doi.org/10.1007/s00033-023-02008-7

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  • DOI: https://doi.org/10.1007/s00033-023-02008-7

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