Related papers: Asymptotic self-similar solutions with a character…
An amplitude equation for an unstable mode in a collisionless plasma is derived from the dynamics on the unstable manifold of the equilibrium $F_0(v)$.\\ The mode eigenvalue arises from a simple zero of the dielectric $\epsilon_{{k}}(z)$;…
The emergence of distinctly sub-diffusive scaling in the vicinity of an anomalous non-thermal fixed point is discussed in a quasi-two-dimensional dipolar Bose gas in the superfluid phase, carrying ensembles of vortices and antivortices with…
The uniform shear flow for the rarefied gas is governed by the time-dependent spatially homogeneous Boltzmann equation with a linear shear force. The main feature of such flow is that the temperature may increase in time due to the shearing…
We present new solutions to the strong explosion problem in a non power law density profi{}le. The unperturbed self similar solutions developed by Sedov, Taylor and Von Neumann describe strong Newtonian shocks propagating into a cold gas…
Spectral singularities and the coherent perfect absorption are two interrelated concepts that have originally been introduced and studied for linear waves interacting with complex potentials. In the meantime, the distinctive asymptotic…
We consider the asymptotic behaviour of small-amplitude gravity water waves in a rectangular domain where the water depth is much smaller than the horizontal scale. The control acts on one lateral boundary, by imposing the horizontal…
We present similarity solutions for adiabatic bubbles that are blown by winds having time independent mechanical luminosities and that are each mass-loaded by the hydrodynamic ablation of distributed clumps. The mass loading is…
We have extended our study of the competition between the drive and stabilization of plasma microinstabilities by sheared flow to include electromagnetic effects at low plasma $\beta$ (the ratio of plasma to magnetic pressure). The extended…
We provide a complete analysis of the asymptotics for the semi-infinite Schur flow: $\alpha_j(t)=(1- |\alpha_j(t)|^2) (\alpha_{j+1}(t)-\alpha_{j-1}(t))$ for $\alpha_{-1}(t)= 1$ boundary conditions and $n=0,1,2,...$, with initial condition…
We study numerically the evolution of an expanding strongly self-coupled real scalar field. We use a conformally invariant action that gives a traceless energy-momentum tensor and is better suited to model the early time behaviour of a…
This paper is concerned with self-similar solutions of the steady Navier-Stokes system in a two-dimensional sector with the no-slip boundary condition. We give necessary and sufficient conditions in terms of the angle of the sector and the…
The flow resulting from a strong ultrarelativistic shock moving through a stellar envelope with a polytrope-like density profile has been studied analytically and numerically at early times while the fluid temperature is relativistic--that…
We characterize the long time behaviour of a discrete-in-time approximation of the volume preserving fractional mean curvature flow. In particular, we prove that the discrete flow starting from any bounded set of finite fractional perimeter…
In this paper we investigate asymptotic isotropization. We derive the asymptotic dynamics of spatially inhomogeneous cosmological models with a perfect fluid matter source and a positive cosmological constant near the de Sitter equilibrium…
A compressible flow characterized by a velocity field $u_x(x,t)=ax/(1+at)$ is analyzed by means of the Boltzmann equation and the Bhatnagar-Gross-Krook kinetic model. The sign of the control parameter (the longitudinal deformation rate $a$)…
We use the perturbation theory to build solitary wave solutions $\phi_\omega(x)e^{-i\omega t}$ to the nonlinear Dirac equation in $\mathbb{R}^n$, $n\ge 1$, with the Soler-type nonlinear term $f(\bar\psi\psi)\beta\psi$, with…
This paper deals with the long-time behavior of solutions of nonlinear reaction-diffusion equations describing formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differentiation in…
We study the asymptotic behavior, as $\gamma$ tends to infinity, of solutions for the homogeneous Dirichlet problem associated to singular semilinear elliptic equations whose model is $$ -\Delta u=\frac{f(x)}{u^\gamma}\,\text{ in }\Omega,…
Holographic RG flows are studied in an Einstein-dilaton theory with a general potential. The superpotential formalism is utilized in order to characterize and classify all solutions that are associated to asymptotically AdS space-times.…
We consider a mean curvature flow in a cylinder with Robin boundary conditions, which can be used to model the interface motion in singular limit problems of the Allen-Cahn equation with nonlinear boundary conditions. It was shown in…