We consider a Cauchy problem for a scalar conservation law in one space dimension with a compactly supported initial datum,

Laws of nature are universal in scope, hold with unfailing regularity, and receive support from a wide array of facts and observations. The Law of Conservation of Information (LCI) is such a law. LCI characterizes the information costs that searches incur in outperforming blind search. Searches that operate by Darwinian selection, for instance, often significantly outperform blind search. But w...

A power-law distribution of the length of perfectly conserved sequence from mouse/human whole-genome intersection and alignment is exhibited. Spatial correlations of these elements within the mouse genome are studied. It is argued that these power-law distributions and correlations are comprised in part by functional noncoding sequence and ought to be accounted for in estimating the statistical...

We consider the parabolic regularization of a scalar conservation law in which the Laplacian operator has been replaced by a fractional power of itself. Using a splitting method, we prove the existence of a solution to the problem and, thanks to the Banach fixed point theorem, its uniqueness and regularity. We also show that, as the regularization vanishes, the solution converge to the entropy ...

A semiclassical transport equation for electrons in a semiconductor crystal is considered. It includes a nonlinear scattering operator modelling electron-phonon interaction. A formal macroscopic limit under the assumption of a small phonon energy is carried out, leading to the so called spherical harmonics expansion (SHE-) model for an energy-dependent distribution function with a scattering op...

In this paper, we study optimal control problems associated with a scalar hyperbolic conservation law modeling the development of ovarian follicles. Changes in the age and maturity of follicular cells are described by a 2D conservation law, where the control terms act on the velocities. The control problem consists in optimizing the follicular cell resources so that the follicular maturity reac...

We introduce a new nonconservative self-organized critical model. This model is equivalent to a quasistatic two-dimensional version of the Burridge-KnopoA spring-block model of earthquakes. Our model displays a robust power-law behavior. The exponent is not universal; rather it depends on the level of conservation. A dynamical phase transition from localized to nonlocalized behavior is seen as ...