Fast diffusion in a porous building material with a nonlocal source

Abstract

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.