Analysis of selfsimilar solutions and a comparison principle for an heterogeneous diffusion cooperative system with advection and non-linear reaction

The present analysis introduces a system of cooperative species formulated with high order parabolic operator, Fisher-KPP reaction and linear advection. Firstly, the oscillatory behaviour solutions is shown to exist shooting method approach. It be highlighted that existence patterns (also called instabilities) an inherent property operators. Afterwards, uniqueness results are provided. most remarkable result, obtained during exercise, related finding particular time-degenerate bound for advection term ensures positivity solutions. This one main as such does not hold operators in general. Indeed, high-order provide may induce negative proximity null state introduced by term. As consequence, comparison principle two Further, positive maximal kernel similar asymptotic compared has been precise assessment done computational exercise. Eventually, permits show principle.