Abstract
In this short note, we investigate the behavior of the solution for a scalar nonlocal semi-linear parabolic equation, in which the nonlocal term acts to conserve the spatial integral of the solution as time evolves. For the solution blowing up in finite time, the blow-up rate is estimated. For the global solution, the global convergence is studied.
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Wang, XL., Tian, FZ. & Li, G. Nonlocal parabolic equation with conserved spatial integral. Arch. Math. 105, 93–100 (2015). https://doi.org/10.1007/s00013-015-0782-1
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DOI: https://doi.org/10.1007/s00013-015-0782-1