Boundary-Value Problem With Saigo Operators for Mixed Type Equation With Fractional Derivative

We set up and solve a non-local problem for a differential equation, which contains the diffusion equation of fractional order. The boundary condition contains a linear combination of generalized operators with the Gauss hypergeometric function in the kernel. For various values of parameters of these operators we write a solution in explicit form.     

On a Frankl-Type Boundary-Value Problem for a Mixed-Type Degenerating Equation

Ukrainian Mathematical Journal - We study the existence and uniqueness of solutions for an analog of the Frankl-type boundary-value problem for a parabolic-hyperbolic-type equation. The uniqueness...     

低温等离子模型中的一个混合型方程的闭Dirichlet问题

描述理想的低温等离子体中电磁波传播的模型是一个椭圆双曲混合型方程.证明了该方程闭Dirichlet问题弱解的存在唯一性.该结果关于区域的几何结构要求较少.由于这里所讨论的方程的奇异性与Keldysh方程的奇异性有相似性质,而后者的奇异性比Tricomi方程更强,因此关于其正则性的研究是很有意义的.作者给出了一个内正则性结果.     

低温等离子模型中的一个混合型方程的闭Dirichlet问题

描述理想的低温等离子体中电磁波传播的模型是一个椭圆双曲混合型方程.证明了该方程闭Dirichlet问题弱解的存在唯一性.该结果关于区域的几何结构要求较少.由于这里所讨论的方程的奇异性与Keldysh方程的奇异性有相似性质,而后者的奇异性比Tricomi方程更强,因此关于其正则性的研究是很有意义的.作者给出了一个内正则性结果.     

On a Problem with Conjugation Conditions for an Equation of Even Order Involving a Caputo Fractional Derivative

Mathematical Notes - A problem for an equation of high even order involving a Caputo fractional derivative in a rectangular domain with conjugation conditions is studied. A criterion for the...     

Boundary Value Problem for a First-Order Partial Differential Equation with Liouville Fractional Derivative

Differential Equations - We consider a first-order partial differential equation with a fractional derivative with respect to one of two independent variables. Fractional differentiation is given...     

非线性分数阶微分方程Robin型边值问题

In this paper,the existence and multiplicity of positive solutions for Robin type boundary value problem of differential equation involving the Riemann-Liouville fractional order derivative are established.     

Inverse Problem for Finding the Order of the Fractional Derivative in the Wave Equation

Mathematical Notes - The paper investigates an inverse problem for finding the order of the fractional derivative in the sense of Gerasimov–Caputo in the wave equation with an arbitrary...     

Oblique Derivative Problem for the Helmholtz Equation in a Disk

We show that the oblique derivative problem for the Helmholtz equation in a disk is uniquely solvable under certain restrictions on the parameter.     

加热下分数阶广义二阶流体的Rayleigh-Stokes问题的一种有效数值方法

考虑加热下分数阶广义二阶流体的Rayleigh-Stokes问题(RSP-HGSGF),提出了一种逼近有界区域内RSP-HGSGF的有效数值方法.并且讨论了所提出方法的稳定性和收敛性.最后,利用数值例子体现数值方法的有效性.     

Directional Derivative Problem for the Telegraph Equation with a Dirac Potential

In the domain Q = [0,∞)×[0,∞) of the variables (x, t), for the telegraph equation with a Dirac potential concentrated at a point (x₀, t₀) ∈ Q, we consider a mixed problem with initial (at t = 0) conditions on the solution and its derivative with respect to t and a condition on the boundary x = 0 which is a linear combination with coefficients depending on t of the solution and its first derivatives with respect to x and t (a directional derivative). We obtain formulas for the classical solution of this problem under certain conditions on the point (x₀, t₀), the coefficient of the Dirac potential, and the conditions of consistency of the initial and boundary data and the right-hand side of the equation at the point (0, 0). We study the behavior of the solution as the direction of the directional derivative in the boundary condition tends to a characteristic of the equation and obtain estimates of the difference between the corresponding solutions.     

Mixed Oblique Derivative Problem for the Helmholtz Equation in a Half-Disk

A mixed oblique derivative boundary value problem is considered for the Helmholtz equation in a half-disk. We prove the unique solvability of this problem for sufficiently large values of the parameter occurring in the equation, the leading part of the inverse operator being constructed explicitly.     

The Oblique Derivative Problem for the Laplace Equation in a Plain Domain

The oblique derivative problem for the Laplace equation is studied in a planar multiply connected domain. The boundary condition has a form where is the unit normal vector, is the unit tangential vector and is a fixed real number. If is a Hölderian function and the corresponding domain has Ljapunov boundary then the classical problem is studied. If on the boundary and the domain has a locally Lipschitz boundary then a solution, which fulfils the boundary condition in the sense of a nontangential limit, is studied. If is a real measure on the boundary and the domain has bounded cyclic variation then a solution in a sense of distributions is studied. The solution is looked for in a form of a linear combination of a single layer potential and an angular potential.     

Local Stability for an Inverse Coefficient Problem of a Fractional Diffusion Equation

Time-fractional diffusion equations are of great interest and importance on describing the power law decay for diffusion in porous media. In this paper, to identify the diffusion rate, i.e., the heterogeneity of medium, the authors consider an inverse coefficient problem utilizing finite measurements and obtain a local Hlder type conditional stability based upon two Carleman estimates for the corresponding differential equations of integer orders.     

分数阶奇异微分方程初值问题正解的存在性

分数阶微分方程解的存在性问题近年来引起了许多人的关注,本文考察了一个非线性分数阶奇异微分方程初值问题正解的存在性,我们的结果削弱了Babakhani, Varsha的假设条件,并要求其非线性项具有一定程度的奇异性．     

On an Inverse Problem for a Parabolic Equation

In this paper, we study the inverse problem of the reconstruction of the right-hand side of special form for a parabolic equation in u in which the coefficients of u _t and u depend on u _(x,t) , with overdetermination given by the integral of the solution over time. The Fredholm property for this problem and the existence and uniqueness theorems in Sobolev spaces are established.