Related papers: On a diffusion equation with rupture

We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each…

Experiments have not only revealed the remarkably long lifetime of nanobubbles, but also demonstrated the diffusive instability of bubbles above micrometers, thus a full-scale physical understanding on the stability of bubbles is in urgent…

The most studies on the stability of foam bubbles investigated the mechanical stability of thin films between bubbles due to the drainage by gravity. In the current work, we take an alternative approach by assuming the rupture of bubbles as…

This paper discusses finite time extinction for a perturbed fast diffusion equation with dynamic boundary conditions. The fast diffusion equation has the characteristic property of decay, such as the solution decays to zero in a finite…

We consider evaporation of pure liquid drops on a thermally conductive substrate. Two evaporative models are considered: one that concentrates on the liquid phase in determining evaporative flux, and the other one that centers on the…

An explicit solution for a growth fragmentation equation with constant dislocation measure is obtained. In this example the necessary condition for the general results in \cite{BW} about the existence of global solutions in the so called…

We call a system bouncing ball billiard if it consists of a particle that is subjected to a constant vertical force and bounces inelastically on a one-dimendional vibrating periodically corrugated floor. Here we choose circular scatterers…

Water usually contains dissolved gases, and because freezing is a purifying process these gases must be expelled for ice to form. Bubbles appear at the freezing front and are then trapped in ice, making pores. These pores come in a range of…

We theoretically investigate the pattern formation observed when a fluid flows over a solid substrate that can dissolve or melt. We use a turbulent mixing description that includes the effect of the bed roughness. We show that the…

The paper presents an analytical description of the growth of a two-component bubble in a binary liquid-gas solution. We obtain asymptotic self-similar time dependence of the bubble radius and analytical expressions for the non-steady…

We prove continuity for bounded weak solutions of a nonlinear nonlocal parabolic type equation associated to a Dirichlet form with a rough kernel. The equation is allowed to be singular at the level zero, and solutions may change sign. If…

An analytic solution for a Fokker-Planck equation that describes propagation of energetic particles through a scattering medium is obtained. The solution is found in terms of an infinite series of mixed moments of particle distribution. The…

Spherical flows are a classic problem in astrophysics which are typically studied from a global perspective. However, much like with accretion discs, there are likely many instabilities and small scale phenomena which would be easier to…

We analyze the Rayleigh equation for the collapse of an empty bubble and provide an explanation for some recent analytical approximations to the model. We derive the form of the singularity at the second boundary point and discuss the…

An impurity particle coupling to its host fluid via inelastic hard sphere collisions is considered. It is shown that the exact equation for its distribution function can be mapped onto that for an impurity with elastic collisions and an…

Fluid phase equilibrium depends on the external constraints imposed on a system. In a closed system with fixed volume, depending on the average density, a vapor bubble may be stable, metastable, or unstable, with respect to the homogeneous…

The collapse of a vapor bubble near a flat solid boundary results in the formation of a jet that is directed towards the boundary. In more complex geometries such as corners, predictions of the collapse cannot be made in a straightforward…

Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for…

An advection--diffusion-limited dissolution model of an object being eroded by a two-dimensional potential flow is presented. By taking advantage of the conformal invariance of the model, a numerical method is introduced that tracks the…

We consider a wide class of fully nonlinear integro-differential equations that degenerate when the gradient of the solution vanishes. By using compactness and perturbation arguments, we give a complete characterization of the regularity of…