Related papers: Shock waves for radiative hyperbolic--elliptic sys…
Relativistic magnetized shocks are a natural source of coherent emission, offering a plausible radiative mechanism for Fast Radio Bursts (FRBs). We present first-principles 3D simulations that provide essential information for the FRB…
In this paper we consider nodal radial solutions $u_\epsilon$ to the problem \[ \begin{cases} -\Delta u=\lambda ue^{u^2+|u|^{1+\epsilon}}&\text{ in }B,\\ u=0&\text{ on }\partial B. \end{cases} \] and we study their asymptotic behaviour as…
The shock structure in a binary mixture of polyatomic Eulerian gases with different degrees of freedom of a molecule is studied based on the multi-temperature model of rational extended thermodynamics. Since the system of field equations is…
Consider a singularly perturbed system $$\epsilon u_t=\epsilon^2 u_{xx} + f(u,x,\epsilon),\quad u\in {\Bbb R}^n,x\in{\Bbb R},t\geq 0. $$ Assume that the system has a sequence of regular and internal layers occurring alternatively along the…
We derive a new formulation of the relativistic Euler equations that exhibits remarkable properties. This new formulation consists of a coupled system of geometric wave, transport, and elliptic equations, sourced by nonlinearities that are…
We study the finite-time blow-up in two variants of the parabolic-elliptic Keller-Segel system with nonlinear diffusion and logistic source. In $n$-dimensional balls, we consider \begin{align*} \begin{cases} u_t = \nabla \cdot…
This note studies classical magnetohydrodynamic shock waves in an inviscid fluidic plasma that is assumed to be a perfect conductor of heat as well as of electricity. For this mathematically prototypical material, it identifies a critical…
The existence and stability of a spherical transonic shock in a hemispherical shell under the three dimensional perturbations of the incoming flows and the exit pressure is established without any further restrictions on the background…
We revisit the first type self-similar solutions for ultrarelativistic shock waves produced by explosions propagating into cold external medium whose density profile decreases with radius as $\rho\propto r^{-k}$. The first type solutions…
Numerical Monte Carlo simulations of the diffusive shock acceleration in the test particle limit are investigated. We simulate high relativistic flow astrophysical plasmas for upstream $\gamma$ $\sim5$ and up to $\gamma$ $\sim1000$. These…
We define compressive and rarefactive waves and give the differential equations describing smooth wave steepening for the compressible Euler equations with a varying entropy profile and general pressure laws. Using these differential…
The current paper is concerned with the forced waves of Keller-Segel chemoattraction systems in shifting environments of the form, \begin{equation} \begin{cases} u_t=u_{xx}-\chi(uv_x)_x +u(r(x-ct)-bu),\quad x\in\mathbb{R}\cr 0=v_{xx}- \nu…
In this work we consider a wide range of energy critical wave equation in 3-dimensional space with radial data. We are interested in exterior scattering phenomenon, in which the asymptotic behaviour of a solutions $u$ to the non-linear wave…
We report a proof that under natural assumptions shock profiles viewed as heteroclinic travelling wave solutions to a hyperbolically regularized system of conservation laws are spectrally stable, if the shock amplitude is sufficiently…
We demonstrate the controllable generation of distinct types of dispersive shock-waves emerging in a quantum droplet bearing environment with the aid of step-like initial conditions. Dispersive regularization of the ensuing hydrodynamic…
The cylindrically converging shock wave was numerically simulated by solving the Euler equations in cylindrical coordinates with TVD scheme and MUSCL approach, using Roe's approximate Riemann solver and super-bee nonlinear limiter. The…
The temporal evolution of weak shocks in radiative media is theoretically investigated in this work. The structure of radiative shocks has traditionally been studied in a stationary framework. Their systematic classification is complex…
Non-stationary Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some exact solutions by means of such a representation.…
In this article, we give a completely constructive proof of the observability/controllability of the wave equation on a compact manifold under optimal geometric conditions. This contrasts with the original proof of Bardos-Lebeau-Rauch,…
Rotating waves are a fascinating feature of a wide array of complex systems, particularly those arising in the study of many chemical and biological processes. With many rigorous mathematical investigations of rotating waves relying on the…