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On the Riemann problem in fractal elastic media

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Abstract

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.

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Funding

Diego Esteban Gutierrez Valencia gratefully acknowledges the financial support of the Postgraduate Study Fellowship of the Consejo Nacional de Ciencia y Tecnología (CONACYT) (Grant Number 962613).

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Authors and Affiliations

  1. Facultad de Matemáticas, Universidad Autónoma de Guerrero, Chilpancingo, Mexico

    Diego Esteban Gutierrez Valencia, Ricardo Abreu Blaya, Martín Patricio Árciga Alejandre & Yudier Peña Pérez

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  1. Diego Esteban Gutierrez Valencia
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  2. Ricardo Abreu Blaya
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  3. Martín Patricio Árciga Alejandre
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  4. Yudier Peña Pérez
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All authors discussed the results and contributed equally to the final manuscript.

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Correspondence to Ricardo Abreu Blaya.

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Valencia, D.E.G., Blaya, R.A., Alejandre, M.P.Á. et al. On the Riemann problem in fractal elastic media. Anal.Math.Phys. 13, 3 (2023). https://doi.org/10.1007/s13324-022-00764-9

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  • DOI: https://doi.org/10.1007/s13324-022-00764-9

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