卷 231, 编号 3 (2018)
- 年: 2018
- 文章: 6
- URL: https://journals.rcsi.science/1072-3374/issue/view/14921
Article
Initial-Boundary Value Problem for the Non-Stationary Radiative Transfer Equation with Fresnel Reflection and Refraction Conditions
摘要
We consider the initial-boundary value problems for the nonstationary radiative transfer equation in a system of semitransparent bodies with boundary and initial data in the complete scale of Lebesgue spaces. We establish the unique solvability of the first initial-boundary value problem, the problem with “shooting conditions,” and the problem with Fresnel reflection and refraction conditions on the body boundaries.
Linear Operator-Differential Equation with Generalized Quasipolynomial on the Right-Hand Side
摘要
We prove an existence and uniqueness theorem for the linear differential equation u′(z) = Au(z)+eγzf(z), where A is a closed operator and f is an entgire vector-valued function of zero exponential type. Bibliography: 10 titles.
A Cliffed Cape Does Not Trap Water Waves in the Sea of Constant Depth
摘要
The water wave problem is considered for a class of semi-infinite domains each having its shore shaped as a cliffed cape. In particular, the free surface of a water domain is supposed to be an infinite sector whose vertex angle is greater than π, whereas the water layer lying under the free surface is of constant depth. Under these assumptions it is shown that there are no trapped mode solutions of the problem for all values of a non-dimensional spectral parameter; in other words, no point eigenvalues are embedded in the continuous spectrum of the problem.
Invertibility of the Radon Kγ-Transform of Lebesgue Integrable Functions with Integer |γ| and an Analog of the Plancherel Formula
摘要
We study invertibility of the Radon Kγ-transform (Kipriyanov–Radon transform) with a natural parameter |γ| and prove an analog of the Plancherel formula.
Radiation Conditions and Integral Representations for Clifford Algebra-Valued Null-Solutions of the Helmholtz Operator
摘要
The goal of this paper is to develop a unified approach to radiation conditions for the entire class of null-solutions of the Helmholtz operator which are Clifford algebra-valued. The latter is an algebraic context which permits the simultaneous consideration of scalarvalued and vector-valued functions, as well as differential forms of any mixed degree. In such a setting, we provide a multitude of novel radiation conditions which naturally contain the classical Sommerfeld and Silver–Müller radiation conditions in the case of null-solutions for the scalar Helmholtz operator and the Maxwell system respectively, and which also encompass as a particular case the radiation condition introduced by McIntosh and Mitrea for perturbed Dirac operators.
Stability of One-Phase States in Variational Problem of the Theory of Elasticity in Two-Phase Media. The Multi-Dimensional Case
摘要
We study the phenomenon of loss of stability of one-phase critical points of the energy functional of a two-phase elastic medium under perturbations of the temperature.