Counterexamples for Uniqueness in Strongly Coupled Parabolic Systems.
Counterexamples to Some Conjectures on the Number of Solutions on Nonlinear Equations.
Counting number of cells and cell segmentation using advection-diffusion equations
We develop a method for counting number of cells and extraction of approximate cell centers in 2D and 3D images of early stages of the zebra-fish embryogenesis. The approximate cell centers give us the starting points for the subjective surface based cell segmentation. We move in the inner normal direction all level sets of nuclei and membranes images by a constant speed with slight regularization of this flow by the (mean) curvature. Such multi- scale evolutionary process is represented by a geometrical...
Co-volume methods for degenerate parabolic problems.
Critical global asymptotics in higher-order semilinear parabolic equations.
Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws
Crossover collision of scroll wave filaments.
Curvature blow-up in perturbations of minimal cones evolving by mean curvature flow
Curvature flows on surfaces
Prompted by recent work of Xiuxiong Chen, a unified approach to the Hamilton-Ricci and Calabi flows on a closed, compact surface is presented, recovering global existence and exponentially fast asymptotic convergence from concentration-compactness results for conformal metrics.