Instability of solutions in a mass-conserving reaction diffusion system
Phys. Rev. E 114, 034225 – Published 29 September, 2026
DOI: https://doi.org/10.1103/5k3q-3yr2
Abstract
We study the spectral stability of traveling and stationary front and pulse solutions in a class of degenerate reaction diffusion systems. We characterize the essential spectrum of the linearized operator in full generality and identify conditions under which it lies entirely in the left half plane. For a number of special cases, we obtain analytical results, including explicit Evans functions and complete spectral descriptions for certain stationary waves. In regimes where analytical methods are not available, we compute the point spectrum numerically using a Riccati–Evans function approach. Our results show that stable traveling fronts can occur, while traveling pulses are generically unstable.
