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- W2084984265 abstract "In this note, we establish the existence of traveling wave solutions to the equations of motions for materials which exhibit long range memory effects. These traveling waves are nontrivial solutions of the integral equation [ (IE)qquad sigma _1 (u(zeta )) + int_0^infty {f(s,u(zeta - s)),ds = c^2 (u(zeta ) - 1)} ] and the boundary condition [ mathop {lim }limits_{zeta to infty } u(zeta ) = 1 ]. Subject to certain hypotheses on $sigma _1 $ and f, the functions which determine the mechanical properties of the material in question, it is shown that if $c^2 geqq sigma '_I (1)$, then (IE) has nontrivial solutions $u( cdot )$ which are bounded and decreasing on $( - infty ,infty )$. These are the shock waves or structured shocks for the materials in question." @default.
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- W2084984265 date "1976-01-01" @default.
- W2084984265 modified "2023-09-23" @default.
- W2084984265 title "Progressive Waves in Materials Exhibiting Long Range Memory" @default.
- W2084984265 cites W2038521961 @default.
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- W2084984265 doi "https://doi.org/10.1137/0130004" @default.
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