A fractional glance to the theory of edge dislocations. (English) Zbl 1518.35585
Indrei, Emanuel (ed.) et al., Geometric and functional inequalities and recent topics in nonlinear PDEs. Virtual conference, Purdue University, West Lafayette, IN, USA, February 28 – March 1, 2021. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 781, 103-135 (2023).
Summary: We revisit some recents results inspired by the Peierls-Nabarro model on edge dislocations for crystals which rely on the fractional Laplace representation of the corresponding equation. In particular, we discuss results related to heteroclinic, homoclinic and multibump patterns for the atom dislocation function, the large space and time scale of the solutions of the parabolic problem, the dynamics of the dislocation points and the large time asymptotics after possible dislocation collisions.
For the entire collection see [Zbl 1512.35008].
For the entire collection see [Zbl 1512.35008].
MSC:
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 74N05 | Crystals in solids |
| 74Q05 | Homogenization in equilibrium problems of solid mechanics |
| 74Q10 | Homogenization and oscillations in dynamical problems of solid mechanics |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B36 | Pattern formations in context of PDEs |
| 82D25 | Statistical mechanics of crystals |
| 26A33 | Fractional derivatives and integrals |
| 35R11 | Fractional partial differential equations |
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