A continuum theory for one-dimensional self-similar elasticity and applications to wave propagation and diffusion

DOI10.1017/S095679251200023XzbMath1257.35177MaRDI QIDQ4902555

Shahram Derogar, Andrzej F. Nowakowski, Gérard A. Maugin, Thomas M. Michelitsch, Mujibur Rahman, Franck C. G. A. Nicolleau

Publication date: 16 January 2013

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

fractional calculusmechanics of fractal structuresself-similar elasticity

Mathematics Subject Classification ID

Linear elasticity with initial stresses (74B10) PDEs in connection with mechanics of deformable solids (35Q74) Green's functions for elliptic equations (35J08)

Related Items (6)

Nonlocal constitutive laws generated by matrix functions: lattice dynamics models and their continuum limits ⋮ A nonlocal constitutive model generated by matrix functions for polyatomic periodic linear chains ⋮ An approach to generalized one-dimensional self-similar elasticity ⋮ A continuum theory for one-dimensional self-similar elasticity and applications to wave propagation and diffusion ⋮ Unnamed Item ⋮ The fractional Laplacian as a limiting case of a self-similar spring model and applications to \(n\)-dimensional anomalous diffusion

Cites Work

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• Quantitative universality for a class of nonlinear transformations
• A fractional model of continuum mechanics
• On a theory of nonlocal elasticity of bi-Helmholtz type and some applications
• The self-similar field and its application to a diffusion problem
• Nonlocal Continuum Field Theories
• A continuum theory for one-dimensional self-similar elasticity and applications to wave propagation and diffusion

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