Related papers: On the construction and properties of weak solutio…
Fast-slow dynamical systems have subsystems that evolve on vastly different timescales, and bifurcations in such systems can arise due to changes in any or all subsystems. We classify bifurcations of the critical set (the equilibria of the…
We explore self-similar hydrodynamic evolution of central voids embedded in an isothermal gas of spherical symmetry under the self-gravity. More specifically, we study voids expanding at constant radial speeds in an isothermal gas and…
This paper presents the results of studies in elaboration of a mathematical model of the cavity-chain slow wave structures. Considered is the problem of coupling of an infinitely long cylindrical cavity chain coupled through centerholes in…
We experimentally investigate the growth dynamics of cavities nucleating during the first stages of debonding of three different model adhesives. The material properties of these adhesives range from a more liquid-like material to a soft…
In this paper we derive an obstacle problem with a free boundary to describe the formation of voids at areas of intense geological folding. An elastic layer is forced by overburden pressure against a V-shaped rigid obstacle. Energy…
Stress-stress correlations in crystalline solids with long-range order can be straightforwardly derived using elasticity theory. In contrast, the `emergent elasticity' of amorphous solids, rigid materials characterized by an underlying…
A liquid subjected to negative pressure is thermodynamically metastable. Confined within a small volume, negative pressure can build up until cavities form spontaneously. The critical negative pressure for cavitation in water has been…
Cavity flow problems in two dimensions, as well as in the axially symmetric three-dimensional case, have been extensively studied in the literature from a qualitative perspective. While numerous results exist concerning minimizers or stable…
We study the Cauchy problem for the $3D$ compressible Euler equations under an arbitrary equation of state with positive speed of sound, aside from that of a Chaplygin gas. For open sets of smooth initial data with non-trivial vorticity and…
We develop a dynamical systems theory for the compressible Navier-Stokes equations based on global in time weak solutions. The following questions will be addressed: Global existence and critical values of the adiabatic constant;…
Many materials of contemporary interest, such as gels, biological tissues and elastomers, are easily deformed but essentially incompressible. Traditional linear theory of elasticity implements incompressibility only to first order and thus…
In this study, novel exact solutions of the Duffing equation with their phase portraits have been proposed and reasoned. It is shown that phase trajectories are initially elliptical and become distorted in the unstable area within the…
Static solutions with a bulk dilaton are derived in the context of six dimensional warped compactification. In the string frame, exponentially decreasing warp factors are identified with critical points of the low energy $\beta$-functions…
A mathematical formulation of an estimation problem of a cavity inside a three-dimensional thermoelastic body using time domain data is considered. The governing equation of the problem is given by a system of equations in the linear theory…
The dynamics of planar crack fronts in hetergeneous media near the critical load for onset of crack motion are investigated both analytically and by numerical simulations. Elasticity of the solid leads to long range stress transfer along…
A constitutive relation between stress and strain relative to a reference state is the basic assumption of elasticity theory. However, in living matter, force generation is governed by motor molecule activity, which does not depend on…
We study the phenomenon of cavitation for the displacement boundary value problem of radial, isotropic compressible elasticity for a class of stored energy functions of the form $W(F) + h(\det F)$, where $W$ grows like $||F||^n$, and $n$ is…
Viscous flows within an elastic structure apply stress on the solid-liquid interface. The stress-field created by the viscous flow can be utilized to counter stress created by external forces and thus may be applied as a tool for delaying…
We develop a theory of self-similar solutions to the critical surface quasi-geostrophic equations. We construct self-similar solutions for arbitrarily large data in various regularity classes and demonstrate, in the small data regime,…
A new self-similar solution describing the dynamical condensation of a radiative gas is investigated under a plane-parallel geometry. The dynamical condensation is caused by thermal instability. The solution is applicable to generic flow…