This work studies the inverse problem of reconstructing a time-dependent heat source in the heat conduction equation using the temperature measurement specified at an internal point. Problems of this type have important applications in several fields of applied science. By the Green’s function...

The greatest relaxation time for an assembly of three-dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is...

Results of numerical simulations of fusion rate d(d,p)t, for low-energy deuteron beam, colliding with deuterated metallic matrix (Phys. Lett. B 547 (2002) 193; Eur. Phys. J. A 13 (2002) 377) confirm analytical estimates given in M. Coraddu et al. (Quantum-tail effect in low energy d+d reaction in...

Using the kinetic equation of subdynamics and the principle of maximal entropy we derive a type of nonlinear Liouville equation (NLE) for project/open quantum systems. The NLE can describe projected (or reduced) density operator, which allows to establish formalism of project Green functions...

A simple derivation of the Galitskii–Yakimets distribution function over momentum is presented. For dense plasmas it contains the law ∼p−8 as a quantum correction to the classical Maxwellian distribution function at large momenta. The integral equation for the width of the spectral...

On the basis of the assumption that atoms play a role of effective Fermions at lattice distribution, the study of the long-range ordering is shown to be reduced to self-consistent consideration of single and collective excitations being relevant to the space distribution of atoms and Fourier...

We investigate an N-dimensional fractional diffusion equation with radial symmetry by taking a spatial and time dependent diffusion coefficient into account, i.e., D˜(r,t)=D(t)r−η with D(t)=Dδ(t)+D¯(t). The equation is considered in a confined region and subjected to time dependent...

We investigate the solutions of a fractional diffusion equation with radial symmetry by using the Green function approach and by taking the N-dimensional case into account. In our analysis, a spatial time-dependent diffusion coefficient is considered, i.e., D(r,t)=Dtδ-1r-θ/Γ(α). The presence...

We prove a maximum principle for local solutions of quasi-linear parabolic stochastic PDEs, with non-homogeneous second order operator on a bounded domain and driven by a space–time white noise. Our method based on an approximation of the domain and the coefficients of the operator, does not...

A collection {B¯(xn,rn)}n⩾1 of pairwise disjoint balls in the Euclidean space Rd is said to be avoidable with respect to a transient process X if the process with positive probability escapes to infinity without hitting any ball. In this paper we study sufficient and necessary conditions for...