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Journals and Conferences
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 consider an elliptic system of Hamiltonian type on a bounded domain. In the superlinear case with critical growth rates we obtain existence and positivity results for solutions under suitable conditions on the linear terms. Our proof is based on an adaptation of the dual variational method as applied before to the scalar case.
We derive the asymptotic behaviour of the ground states of a system of two coupled semilinear Poisson equations with a strongly indeenite variational structure in the critical Sobolev growth case.
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)
We consider the initial value problem for the equation u t = u xx +H(u), where H is the Heaviside graph, on a bounded interval with Dirichlet boundary conditions, and discuss existence, regularity and uniqueness of solutions and interfaces .
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)