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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Veröffentlicht in:Analysis and mathematical physics 2023-02, Vol.13 (1), Article 3
Hauptverfasser: Valencia, Diego Esteban Gutierrez, Blaya, Ricardo Abreu, Alejandre, Martín Patricio Árciga, Pérez, Yudier Peña
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Analytic functions
Boundary value problems
Cauchy problems
Elastic media
Fractals
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
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Zusammenfassung: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