Abstract
Continuous and discontinuous one-dimensional waves of stationary profile are studied in non-linearly hereditary rods, where the heredity kernel is not assumed to be regular (i.e., the existence of a singularity is allowed for in the kernel, an integrable singularity as t → +0). Appropriate near-front asymptotic forms are found. As is well-known /1/, strong discontinuities cannot propagate in hereditary media with singular kernels in a linear situation. Consequently, the very possibility of the existence of solutions with strong discontinuities in the non-linear singular case is not totally trivial.
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