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The harmonic map heat flow is a model for nematic liquid crystals and also has origins in geometry. We present an analysis of the asymptotic behaviour of singularities arising in this flow for a special class of solutions which generalises a known (radially symmetric) reduction. Specifically , the rate at which blowup occurs is investigated in settings with(More)
Specific product formation rates and cellular growth rates are important maximization targets in biotechnology and microbial evolution. Maximization of a specific rate (i.e. a rate expressed per unit biomass amount) requires the expression of particular metabolic pathways at optimal enzyme concentrations. In contrast to the prediction of maximal product(More)
We consider a free-boundary problem for the heat equation which arises in the description of premixed equi-diiusional ames in the limit of high activation energy. It consists of the heat equation u t = u; u > 0; posed in an apriori unknown set Q T = R N (0; T) for some T > 0 with boundary conditions on the free lateral boundary ? = @ \ Q T (the ame front):(More)
We consider non-negative solutions on the half-line of the thin film equation h t + (h n h xxx) x = 0, which arises in lubrication models for thin viscous films, spreading droplets and Hele–Shaw cells. We present a discussion of the boundary conditions at x = 0 on the basis of formal and modelling arguments when x = 0 is an edge over which fluid can drain.(More)
We construct compactly supported self-similar solutions of the Modiied Porous Medium Equation (MPME) u t = u m for u m > 0 (1 + "))u m for u m < 0: They have the form u(x; t) = t ? U(x t ?); where the similarity exponents and depend on ", m and the dimension N. This corresponds to what is known in the literature as anomalous exponents or self-similarity of(More)
In this paper we are interested in a rigorous derivation of the Kuramoto-Sivashinsky equation (K–S) in a Free Boundary Problem. As a paradigm, we consider a two-dimensional Stefan problem in a strip, a simplified version of a solid-liquid interface model. Near the instability threshold, we introduce a small parameter ε and define rescaled variables(More)