Abstract
This paper is considered with a three-dimensional pyramidal traveling wave of the homogeneous reaction–diffusion equation with a compact obstacle in R3. The long-time behavior of the entire solution derived from a pyramidal traveling wave after passing an obstacle is explored. Mainly relying on auxiliary functions, some new forms of super- and sub-solutions with good characteristics are proposed, and some properties of the pyramidal traveling wave are obtained. The results show that when the propagation of the entire solution is complete, the solution will recover to the same pyramidal traveling wave as before.
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