On the Riemann problem in fractal elastic media

被引：3

作者：

Gutierrez Valencia, Diego Esteban ^{[1
]}

Abreu Blaya, Ricardo ^{[1
]}

Arciga Alejandre, Martin Patricio ^{[1
]}

Pena Perez, Yudier ^{[1
]}

机构：

[1] Univ Autonoma Guerrero, Fac Matemat, Chilpancingo, Mexico

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2023年 / 13卷 / 01期

关键词：

Riemann problem; Kolosov-Muskhelishvili formula; Linear elasticity; CONJUGATION PROBLEM; 2ND-ORDER;

D O I：

10.1007/s13324-022-00764-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study a kind of Riemann problem for the Lame-Navier system in the plane on a smooth as well as on a fractal closed contour. By using the Kolosov-Muskhelisvili formula, we reduce this problem to a pair of Riemann boundary value problems for analytic functions, and after that we get the necessary and sufficient conditions for the solvability of the problem and obtain explicit formulas for its solution.

引用

页数：15

共 20 条

[1] A Riemann jump problem for biharmonic functions in fractal domains [J].

Abreu Blaya, Ricardo .

ANALYSIS AND MATHEMATICAL PHYSICS, 2021, 11 (01)

[2] Analytic Riemann boundary value problem on h-summable closed curves [J].

Abreu Blaya, Ricardo ;

Bory Reyes, Juan ;

Moreno Garcia, Tania ;

Pena Perez, Yudier .

APPLIED MATHEMATICS AND COMPUTATION, 2014, 227 :593-600

[3]

[Anonymous], 1995, Curves and Fractal Dimension

[4] On an effective solution of the Riemann problem for the second-order improperly elliptic equation in the rectangle [J].

Babayan, Armenak O. ;

Raeisian, Seyed Mohammadali .

ADVANCES IN DIFFERENCE EQUATIONS, 2013,

[5] The Doubly Periodic "Jump" Problem for a Second-Order Linear Elliptic Equation With Constant Coefficients [J].

Bikchantaev, I. A. .

RUSSIAN MATHEMATICS, 2019, 63 (02) :11-17

[6] Periodic Conjugation Problem for Linear Elliptic Equations of Second Order with Constant Coefficients [J].

Bikchantaev I.A. .

Lobachevskii Journal of Mathematics, 2018, 39 (2) :165-168

[7]

Dolzhenko EP., 1970, AM MATH SOC TRANSL, V97, P33

[8]

Feng Lin, 2011, 2011 International Conference on Multimedia Technology, P2330

[9]

Gakhov F. D., 1977, Boundary value problem

[10] Riemann boundary-value problem for doubly-periodic bianalytic functions [J].

Han, Huili ;

Liu, Hua ;

Wang, Yufeng .

BOUNDARY VALUE PROBLEMS, 2018,

← 1 2 →