Heterogeneous Diffusion, Stability Analysis, and Solution Profiles for a MHD Darcy–Forchheimer Model

In the presented analysis, a heterogeneous diffusion is introduced to magnetohydrodynamics (MHD) Darcy–Forchheimer flow, leading an extended model. The introduction of generalized was proposed by Cohen and Murray study energy gradients in spatial structures. addition, Peletier Troy, on one side, Rottschäfer Doelman, other have general (of fourth-order derivative) oscillatory patterns close critical points induced reaction term. study, analytical conceptions problem with diffusions are introduced. First, existence uniqueness solutions provided. Afterwards, stability aiming characterize asymptotic convergent condition for patterns. Dedicated solution profiles explored, making use Hamilton–Jacobi type equation. may induce be negative, null equilibrium; hence, precise inner region positive obtained.