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We consider the Helmholtz problem in the context of the evolution of uniforminitial distribution of a physical attribute in general porous media subject toa partially absorbing boundary condition. Its spectral property as a reflectionof the boundary geometry has been widely exploited, such as in biological andgeophysical applications. We consider the situation where the criticalassumptions which enable such applications break down. Specifically, what arethe consequences of an inhomogeneous absorption strength? By means ofperturbation theory, exact theoretical results, and numerical simulations onrandom sphere packs, we identify the regions of parameter space in which suchinhomogeneity is important and those in which it is not. Our findings shedlight on the issue that limits the mapping between the diffusion/relaxationspectrum and the underlying boundary geometry.

Aspects of diffusive-relaxation dynamics with a non-uniform, partially absorbing boundary in general porous media