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In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to th...
Characteristics of Mode I crack near the interface of elasticity matched but plasticity and strength mismatched materials differ from those of the crack in a homogenous body. Interface body of differe...
The paper presents a model of a dynamic crack with a wavy surface. So far, theoretical analysis of crack front waves has been performed only for in-plane perturbations of the crack front. In the prese...
The shape of a crack front propagating through a thin sample is studied using a phase field model. The model is shown to have a well defined sharp interface limit. The crack front is found to be an el...
By the methods of the theory of complex functions, dynamic propagation problems concerning mode Ⅲ crack were investigated. Analytical solutions can be obtained by the approaches of self-similar functi...

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