Fast diffusion in a porous building material with a nonlocal source

Xiao Zhang, Chunxiao Yang and Jinge Yang

Applied Mathematics and Computation, 2020, vol. 382, issue C

Abstract: Fast diffusion is of great importance in concrete solidification, and this paper suggests a modified Fick law to deduce a fast diffusion equation with a nonlocal source. Its global and non-global solutions are obtained, and the critical Fujita exponent and second critical exponent are discussed. A numerical example is given to elucidate the basic properties of the fast diffusion process. The theoretical results shed a promising light on an extremely fast solidification of a concrete in building an artificial island or an urgent repairing in an accident.

Keywords: Fast diffusion; Critical exponent; Global existence; Blow-up; Fractal calculus; Fast solidification; Fast diffusion law; Catastrophe (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:382:y:2020:i:c:s0096300320302939

DOI: 10.1016/j.amc.2020.125327

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