Inverse Problems for Degenerate Fractional Integro-Differential Equations

This paper deals with inverse problems related to degenerate fractional integro-differential equations in Banach spaces. We study existence, uniqueness and regularity of solutions to the problem, claiming to extend well known studies for the case of non-fractional equations. Our method is based on transforming the inverse problem to a direct problem and identifying the conditions under which this direct problem has a unique solution. The conditions under which the unique strict solution can be compared with the case of a mild solution, obtained in previous studies under quite restrictive requirements, are on the underlying functions. Applications from partial differential equations are given to illustrate our abstract results.

ONCE AGAIN ABOUT THE PROBLEM “4/3”

It is shown that the problem "4/3" or the problem of electromagnetic mass has a strict solution only if the fields are instantaneous. This result is valid in both the classical and relativistic variants. The hypothesis of the existence of a physical ether is introduced, which allows us to explain the constancy of the speed of light in inertial reference systems and features of instantaneous action at a distance.

Identifications for General Degenerate Problems of Hyperbolic Type in Hilbert Spaces

In a Hilbert space X, we consider the abstract problem M∗ddt(My(t))=Ly(t)+f(t)z,0≤t≤τ,My(0)=My0, where L is a closed linear operator in X and M∈L(X) is not necessarily invertible, z∈X. Given the additional information Φ[My(t)]=g(t) wuth Φ∈X∗, g∈C1([0,τ];C). We are concerned with the determination of the conditions under which we can identify f∈C([0,τ];C) such that y be a strict solution to the abstract problem, i.e., My∈C1([0,τ];X), Ly∈C([0,τ];X). A similar problem is considered for general second order equations in time. Various examples of these general problems are given.

Advanced Approach for Radiation Transport Description in 3D Collisional-radiative Models

The description of radiation transport phenomena in the frames of collisional-radiative models requires the solution of Holstein-Biberman equation. An advanced solutuion method for 3D plasma obejcts is proposed. The method is applicable for various line contours in a wide range of absorption coefficients. Developed approach is based on discretization of the arbitrary plasma volume on a Cartesian voxel grid. Transport of photons between the cells is computed using the ray traversal algorithm by Amanatides [1]. Solution of the particle balance equations with computed in advance radiative transfer matrix is demonstrated for various typical arc shapes, like e.g. free-burning arc and cylindric arc. Results are compared with corresponding calculations using previously developed approaches. As the method is suited for finite geometries and allows for a strict solution of the radiation transport equation, applicability ranges of previous approximations can be specified.

Resolution in hölder spaces of an elliptic problem in an unbounded domain

In this paper we give new results concerning the maximal regularity of the strict solution of an abstract second-order differential equation, with non-homogeneous boundary conditions of Dirichlet type, and set in an unbounded interval. The right-hand term of the equation is a Hölder continuous function.