180 citations · 1.3k across the 65 of their papers we have counts for
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The Gamma-limit of the two-dimensional Ohta-Kawasaki energy. II. Droplet arrangement at the sharp interface level via the renormalized energy
Dorian Goldman, Cyrill B. Muratov, Sylvia Serfaty
This is the second in a series of papers in which we derive a -expansion for the two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion known as the Ohta-Kawasa…
On an isoperimetric problem with a competing non-local term. II. The general case
Hans Knuepfer, Cyrill B. Muratov
This paper is the continuation of [H. Knüpfer and C. B. Muratov, Commun. Pure Appl. Math. (2012, to be published)]. We investigate the classical isoperimetric problem modified by a…
Threshold phenomena for symmetric decreasing solutions of reaction-diffusion equations
C. B. Muratov, X. Zhong
We study the long time behavior of solutions of the Cauchy problem for nonlinear reaction-diffusion equations in one space dimension with the nonlinearity of bistable, ignition or…
Asymptotic properties of ground states of scalar field equations with a vanishing parameter
Vitaly Moroz, Cyrill B. Muratov
We study the leading order behaviour of positive solutions of the equation -Δu +\varepsilon u-|u|^{p-2}u+|u|^{q-2}u=0,\qquad x\in\R^N, where , and when $\varepsilon…
Self-similarity and long-time behavior of solutions of the diffusion equation with nonlinear absorption and a boundary source
Peter V. Gordon, Cyrill B. Muratov
This paper deals with the long-time behavior of solutions of nonlinear reaction-diffusion equations describing formation of morphogen gradients, the concentration fields of molecul…