Reaction-diffusion waves in hydro-mechanically coupled porous solids as
a precursor to instabilities
Here, we extend the Fisher-Kolmogorov-Petrovsky-Piskunov equation to
capture the interplay of multiscale and multiphysics coupled processes.
We use a minimum of two coupled reaction-diffusion equations with
additional nonlocal terms that describe the coupling between scales
through mutual cross-diffusivities and regularise the ill-posed
reaction-self-diffusion system. Applying bifurcation theory we suggest
that geological patterns can be interpreted as physical representations
of two classes of well-known instabilities: Turing instability, Hopf
bifurcation, and a new class of complex soliton-like waves. The new
class appears for small fluid release reactions rates which may, for
negligible self-diffusion, lead to an extreme focusing of wave intensity
into a short sharp earthquake-like event. We propose a first step
approach for detection of these dissipative waves, expected to precede a
large scale instability.