Time Adaptive Numerical Solution of a Highly Degenerate Diffusion–Reaction Biofilm Model Based on Regularisation
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DOI: 10.1007/s10915-017-0483-y
Abstract: We consider a quasilinear degenerate diffusion–reaction system that describes biofilm formation. The model exhibits two non-linear effects: a power law degeneracy as one of the dependent variables vanishes and a super diffusion singularity as it… read more here.
Keywords: regularisation; diffusion; diffusion reaction; model ... See more keywords
Fundamental Solution to 1D Degenerate Diffusion Equation with Locally Bounded Coefficients
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.125979
Abstract: In this work we study the degenerate diffusion equation $\partial_{t}=x^{\alpha}a\left(x\right)\partial_{x}^{2}+b\left(x\right)\partial_{x}$ for $\left(x,t\right)\in\left(0,\infty\right)^{2}$, equipped with a Cauchy initial data and the Dirichlet boundary condition at $0$. We assume that the order of degeneracy at 0 of… read more here.
Keywords: locally bounded; diffusion; left right; right left ... See more keywords