Related papers: Steady-State Solutions in Nonlinear Diffusive Shoc…
We consider a class of reaction-diffusion equations with a stochastic perturbation on the boundary. We show that in the limit of fast diffusion, one can rigorously approximate solutions of the system of PDEs with stochastic Neumann boundary…
Collisionless shocks are often studied in two spatial dimensions (2D), to gain insights into the 3D case. We analyze diffusive shock acceleration for an arbitrary number $N\in\mathbb{N}$ of dimensions. For a non-relativistic shock of…
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
Diffusive Shock Acceleration (DSA) cannot efficiently accelerate particles without the presence of self-consistently generated or pre-existing strong turbulence ($ \delta B/B \sim 1 $) in the vicinity of the shock. The problem we address in…
We consider two examples of solutions of the equations of motion of scalar field theories with higher derivatives. These are the cosmology of the rolling tachyon and static spherically symmetric solutions of the scalar field in flat space.…
Particle acceleration is an ubiquitous phenomenon in astrophysical and space plasma. Diffusive shock acceleration (DSA) and stochastic turbulent acceleration are known to be the possible mechanisms for producing very high energetic…
We present an analysis of the stationary distributions of run-and-tumble particles trapped in external potentials in terms of a thermophoretic potential, that emerges when trapped active motion is mapped to trapped passive Brownian motion…
Convection-diffusion problem are the base for continuum mechanics. The main features of these problems are associated with an indefinite operator the problem. In this work we construct unconditionally stable scheme for non-stationary…
Finding the injection threshold for diffusive shock acceleration (DSA) of electrons in collisionless shocks has been a longstanding unsolved problem. Using first-principles kinetic simulations, we identify the conditions for electron…
These notes present the fundamentals of Fermi acceleration at shocks, with a special attention to the role that supernova remnants have in producing Galactic cosmic rays. Then, the recent discoveries in the theory of diffusive shock…
We present a general model allowing one to calculate the distribution function of energetic particles in the interstellar medium, and hence any relevant nuclear reaction rate, for any given time-dependent injection function, as well as in…
This article is devoted to stationary solutions of Euler's equation on a rotating sphere, and to their relevance to the dynamics of stratospheric flows in the atmosphere of the outer planets of our solar system and in polar regions of the…
Diffusive shock acceleration (DSA) of particles at collisionless shocks is the major accepted paradigm about the origin of cosmic rays (CRs). As a theory it was developed during the late 1970s in the so-called test-particle case. If one…
Planar travelling waves on $\mathbb R^d,$ with $ d\geq 2,$ are shown to persist in systems of reaction-diffusion equations with multiplicative noise on significantly long timescales with high probability, provided that the wave is orbitally…
This paper is concerned with the stability of stationary solutions of the conservation law $\partial_t u + \mathrm{div}_y A(y,u) -\Delta_y u=0$, where the flux $A$ is periodic with respect to its first variable. Essentially two kinds of…
Context: Typical space plasmas contain spatially and temporally variable turbulent electromagnetic fields. Understanding the transport of energetic particles and the acceleration mechanisms for charged particles is an important goal of…
In this study, we investigate the dynamics of moving fronts in three-dimensional spaces, which form as a result of in-situ combustion during oil production. This phenomenon is also observed in other contexts, such as various autowave models…
Particle acceleration in the dynamically evolving environment of Supernova Remnants is discussed in the framework of a genuinely time-dependent nonlinear theory, assuming spherical symmetry. As a consequence the dependence of injection on…
This paper is concerned with the existence and qualitative properties of pulsating fronts for spatially periodic reaction-diffusion equations with bistable nonlinearities. We focus especially on the influence of the spatial period and,…