Carpio Rodríguez, Ana MaríaChapman, S. J.Velázquez, J. J. L.2023-06-202023-06-202001Carpio Rodríguez, A. M., Chapman, S. J. y Velázquez, J. J. L. «Pile-Up Solutions for Some Systems of Conservation Laws Modelling Dislocation Interaction in Crystals». SIAM Journal on Applied Mathematics, vol. 61, n.o 6, enero de 2001, pp. 2168-99. DOI.org (Crossref), https://doi.org/10.1137/S0036139999364347.0036-139910.1137/S0036139999364347https://hdl.handle.net/20.500.14352/57217Some continuum models for dislocation interactions in a simple crystal geometry are studied. The simplest models are mixed systems ofconservation laws which are shown to exhibit singularities and instabilities. These are then regularized, leading to parabolic free-boundary problems. In both cases, solutions describing the formation of structures such as dislocation pile-ups are discussed.engjournal articlehttps//doi.org/10.1137/S0036139999364347http://epubs.siam.org/siap/resource/1/smjmap/v61/i6/p2168_s1?isAuthorized=noopen access517.9530.1Dislocation dynamicsDegenerate systems of conservation lawsFree-boundary problemsPattern formationFísica matemáticaEcuaciones diferenciales1202.07 Ecuaciones en Diferencias