Semigroup theory and asymptotic profiles of solutions for a higher-order Fisher-KPP problem in R^N

We study a reaction-diffusion problem formulated with higher-order operator, non-linear advection, and Fisher-KPP reaction term depending on the spatial variable. The operator induces solutions to oscillate in proximity of an equilibrium condition. Given this oscillatory character, are studied set bounded domains. introduce new extension that allows us open domain RN, but departing from sequence analysis about regularity is built based semigroup theory. In approach, interpreted as abstract evolution given by continuous operator. Afterward, asymptotic profiles Hamilton-Jacobi equation obtained single point exponential scaling. Finally, numerical assessment, function bvp4c Matlab, introduced discuss validity hypothesis.