3 papers
math.AP2020
Conditional uniqueness of solutions to the Keller-Rubinow model for Liesegang rings in the fast reaction limit
Zymantas Darbenas, Rein van der Hout, Marcel Oliver
We study the question of uniqueness of weak solution to the fast reaction limit of the Keller and Rubinow model for Liesegang rings as introduced by Hilhorst et al. (J. Stat. Phys.…
math.AP2019
Long-time asymptotics of solutions to the Keller-Rubinow model for Liesegang rings in the fast reaction limit
Zymantas Darbenas, Rein van der Hout, Marcel Oliver
We consider the Keller--Rubinow model for Liesegang rings in one spatial dimension in the fast reaction limit as introduced by Hilhorst, van der Hout, Mimura, and Ohnishi in 2007.…
math.CA2019
Breakdown of Liesegang precipitation bands in a simplified fast reaction limit of the Keller-Rubinow model
Zymantas Darbenas, Marcel Oliver
We study solutions to the integral equation \[ ω(x) = Γ- x^2 \int_{0}^1 K(θ) \, H(ω(xθ)) \, \mathrm d θ\] where , is a weakly degenerate kernel satisfying, among other pro…