On the Riemann problem in fractal elastic media

On the Riemann problem in fractal elastic media

In this paper we study a kind of Riemann problem for the Lamé–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 t...

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Bibliographic Details
Published in:Analysis and mathematical physics Vol. 13; no. 1
Main Authors: Valencia, Diego Esteban Gutierrez, Blaya, Ricardo Abreu, Alejandre, Martín Patricio Árciga, Pérez, Yudier Peña
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01-02-2023
Springer Nature B.V
Subjects:
Analysis
Analytic functions
Boundary value problems
Cauchy problems
Elastic media
Fractals
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
28A80
30G35
Riemann problem
Kolosov–Muskhelishvili formula
Linear elasticity
30E25
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Summary:In this paper we study a kind of Riemann problem for the Lamé–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.
ISSN:1664-2368
1664-235X
DOI:10.1007/s13324-022-00764-9