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The class of strongly quasiconvex functions was introduced in the famous paper of B.T. Polyak in 1966. It is the natural extension of the class of strongly convex functions, its applications emcompass...
New evidence confirms that first-ever pictures do capture the birth of a pair of planets orbiting the star PDS 70.Using a new infrared pyramid wavefront sensor for adaptive optics correction at the...
New evidence confirms that first-ever pictures do capture the birth of a pair of planets orbiting the star PDS 70.Using a new infrared pyramid wavefront sensor for adaptive optics correction at the...
We consider Navier-Stokes equations for compressible viscous fluids in one dimension. It is a well known fact that if the initial datum are smooth and the initial density is bounded by below by a posi...
In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to th...
We study a class of mean curvature equations −Mu = H +λup where M denotes the mean curvature operator and for p ≥ 1. We show that there exists an extremal parameter λ∗ such that this equat...
We consider an equation modeling the evolution of a viscous liquid thin film wetting a horizontal solid substrate destabilized by an electric field normal to the substrate. The effects of the electric...
We prove the existence and give the asymptotic behavior of non local fronts in homogeneous media.
We establish the global existence of weak solutions to a class of kinetic flocking equations. The models under conideration include the kinetic Cucker-Smale equation [6, 7] with possibly non-symmetric...
Earthquake prediction based on precursors can aim to provide fully quantified, time-varying, synoptic forecasts, which do not depart from physical and geological principles, and are amenable to formal...
Given a potential of pair interaction and a value of activity, one can consider the Gibbs distribution in a finite domain Λ ⊂ Z d . It is well known that for small values of activity there...
We show that the set of diagonal similarity scalings that minimize the scaled singular value of a matrix is nonempty and bounded if and only if the matrix that is being scaled is irreducible. For an i...
We consider a model for the propagation of a subsonic detonation wave through a porous medium introduced by Sivashinsky [8]. We show that it admits travelling wave solutions that converge in the limit...
A one-dimensional system describing the propagation of low Mach number flames in sprays is studied. We show that pulsating waves may exist when the droplet distribution in the unburnt region is spatia...
We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-fro...

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