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The paper considers parabolic equations in non-divergent form with discontinuous coefficients at higher derivatives. Their investigation is most complicated because, in general, in the case of discontinuous coefficients, the uniqueness of a…
Emulsions are common in many natural and industrial settings. Recently, much attention has been put on understanding the dynamics of turbulent emulsions. This paper reviews some recent studies of emulsions in turbulent Taylor-Couette flow,…
In this paper a quantum mechanical description of the assembly/disassembly process for microtubules is proposed. We introduce creation and annihilation operators that raise or lower the microtubule length by a tubulin layer. Following that,…
We derive precise transformation formulas for synthetic lower Ricci bounds under time change. More precisely, for local Dirichlet forms we study how the curvature-dimension condition in the sense of Bakry-Emery will transform under time…
Plasmon and polariton modes are derived for an ideal semi-infinite (half-space) plasma and an ideal plasma slab by using a general, unifying procedure, based on equations of motion, Maxwell's equations and suitable boundary conditions.…
This article describes the fuzzy conformable fractional derivative which is based on generalized Hukuhara differentiability. On these topics, we prove a number of properties concerning this type of differentiability. In addition, fuzzy…
This paper provides a new numerical strategy to solve fractional in space reaction-diffusion equations on bounded domains under homogeneous Dirichlet boundary conditions. Using the matrix transform method the fractional Laplacian operator…
We apply the Hilbert transform to the physics of internal waves in two-dimensional fluids. Using this demodulation technique, we can discriminate internal waves propagating in different directions: this is very helpful in answering several…
The Smith-Purcell radiation is usually measured when an electron passes over the grating of metallic stripes. However, for high frequencies (exceeding the plasma frequency of the grating material) none material could be treated as a…
In this article, we study the unique determination of convection term and the time-dependent density coefficient appearing in a convection-diffusion equation from partial Dirichlet to Neumann map measured on boundary.
A constructive approach to theory of diffusion processes is proposed, which is based on application of both the symmetry analysis and method of modelling functions. An algorithm for construction of the modelling functions is suggested. This…
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in…
First we introduce and analyze a convergent numerical method for a large class of nonlinear nonlocal possibly degenerate convection diffusion equations. Secondly we develop a new Kuznetsov type theory and obtain general and possibly optimal…
A distributed order fractional diffusion equation is considered. Distributed order derivatives are fractional derivatives that have been integrated over the order of the derivative within a given range. In this paper sub-diffusive cases are…
The self-similar asymptotics for solutions to the drift-diffusion equation with fractional dissipation, coupled to the Poisson equation, is analyzed in the whole space. It is shown that in the subcritical and supercritical cases, the…
The roles of nuclear deformation and neutron transfer in sub-barrier capture process are studied within the quantum diffusion approach. The change of the deformations of colliding nuclei with neutron exchange can crucially influence the…
We provide the proof of convergence of the directional diffusion splitting scheme for two-dimensional parabolic and elliptic advection-diffusion-reaction problems with certain restrictions on problem data
With neutron star applications in mind, we developed a theory of diffusion in mixtures of superfluid, strongly interacting Fermi liquids. By employing the Landau theory of Fermi liquids, we determined matrices that relate the currents of…
For given strongly local Dirichlet forms with possibly degenerate symmetric (sub)-elliptic matrix, we show the existence of weak solutions to the stochastic differential equations (associated with the Dirichlet forms) starting from all…
This paper is concerned with the existence of positive solutions for a fractional population model with the homogeneous Dirichlet condition on the exterior of a bounded domain. The approach is based on the sub-super solutions method. Our…