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Lifespan, asymptotic behavior and ground-state solutions to a nonlocal parabolic equation

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Abstract

We consider a nonlocal parabolic equation, which was studied in Liu and Ma (Nonlinear Anal 110:141–156, 2014), Li and Liu (J Math Phys 58:101503, 2017). By exploiting the boundary condition and the variational structure of the equation, we obtain the lifespan for the blow-up solutions, decay estimation and asymptotic behavior for the global solutions and ground-state solutions for the stationary solutions. The results generalize the former studies on this equation.

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  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Jun Zhou

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  1. Jun Zhou
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Correspondence to Jun Zhou.

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The research has been supported by NSFC Grant 11201380 and Basic and Advanced Research Project of CQC-STC Grant cstc2016jcyjA0018.

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Zhou, J. Lifespan, asymptotic behavior and ground-state solutions to a nonlocal parabolic equation. Z. Angew. Math. Phys. 71, 28 (2020). https://doi.org/10.1007/s00033-020-1251-7

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  • DOI: https://doi.org/10.1007/s00033-020-1251-7

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