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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...
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...
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 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...
The focus of this dissertation is the existence, stability, and resulting dynamical evolution of localized stationary solutions to Nonlinear Schr¨odinger (NLS) equations with periodic confining potent...
Let p be a prime, P a finite p-group and F a Frobenius P-category. The question on the existence of a suitable category L^sc extending the full subcategory of F over the set of F-selfcentralizing subg...
Let $D=(V(D), A(D))$ be a digraph and $k \ge 2$ an integer. We say that $D$ is $k$-quasi-transitive if for every directed path $(v_0, v_1,..., v_k)$ in $D$, then $(v_0, v_k) \in A(D)$ or $(v_k, v_0) \...

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