We consider an initial-boundary value problem for a degenerate pseudoparabolic regularization of a nonlinear forward-backward-forward parabolic equation, with a bounded nonlinearity which is increasing at infinity. We prove existence of suitably defined nonnegative solutions of the problem in a space of Radon measures. Solutions satisfy several monotonicity and regularization properties; in particular, their singular part is nonincreasing and may disappear in finite time.

Background Cell organization is governed and maintained via specific interactions among its constituent macromolecules. Comparison of the experimentally determined protein interaction networks in different model organisms has revealed little conservation of the specific edges linking ortholog proteins. Nevertheless, some topological characteristics of the graphs representing the networks - namely non-random degree distribution and high clustering coefficient - are shared by networks of distantly related organisms.

We study the Poiseuille flow of a soft-glassy material above the jamming point, where the material flows like a complex fluid with Herschel-Bulkley rheology. Microscopic plastic rearrangements and the emergence of their spatial correlations induce cooperativity flow behavior whose effect is pronounced in presence of confinement. With the help of lattice Boltzmann numerical simulations of confined dense emulsions, we explore the role of geometrical roughness in providing activation of plastic events close to the boundaries.

In [Comm. Appl. Math. Comput. Sci., 4 (2009), pp. 153-175], Barenblatt presents a model for partial laminarization and acceleration of shear flows by the presence of suspended particles of different sizes, and provides a formal asymptotic analysis of the resulting velocity equation. In the present paper we revisit the model. In particular we allow for a continuum of particle sizes, rewrite the velocity equation in a form which involves the Laplace transform of a given function or measure, and provide several rigorous asymptotic expansions for the velocity.

Spatial and velocity statistics of heavy point-like particles in incompressible, homogeneous, and isotropic three-dimensional turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number Re-lambda similar to 200 and Re-lambda similar to 400, corresponding to resolutions of 512(3) and 2048(3) grid points, respectively. Particles Stokes number values range from St approximate to 0.2 to 70.

We consider a cell growth model involving a nonlinear system of partial differential equations which describes the growth of two types of cell populations with contact inhibition. Numerical experiments show that there is a parameter regime where, for a large class of initial data, the large time behaviour of the solutions is described by a segregated travelling wave solution with positive wave speed c.

We analyze the dynamics of small particles vertically confined, by means of a linear restoring force, to move within a horizontal fluid slab in a three-dimensional (3D) homogeneous isotropic turbulent velocity field. The model that we introduce and study is possibly the simplest description for the dynamics of small aquatic organisms that, due to swimming, active regulation of their buoyancy, or any other mechanism, maintain themselves in a shallow horizontal layer below the free surface of oceans or lakes.

The paper concerns a continuous model governed by a ODE system originated by a discrete duopoly model with bounded rationality, based on constant conjectural variation. The aim of the paper is to show (i) the existence of an absorbing set in the phase space; (ii) linear stability analysis of the critical points of the system; (iii) nonlinear, global asymptotic stability of equilibrium of constant conjectural variation.

A general framework is developed to investigate the properties of useful choices of stationary spacelike slicings of stationary spacetimes whose congruences of timelike orthogonal trajectories are interpreted as the world lines of an associated family of observers, the kinematical properties of which in turn may be used to geometrically characterize the original slicings.