Geodesic
Regularization of a nonstandard Cauchy problem for a dynamic Lame system
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2020), pp. 54-63

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We consider a Cauchy problem for the dynamic systems Lame in a cylinder $G_T=D\times(0,T)$ over a domain $D$ in $R^3$ with data on a strip lying on the lateral surface. The strip is of the form $S\times(0,T)$, where $S-$ is an open subset of the boundary of $D$. The problem is ill-posed. Under natural restrictions on the configuration of $S$ we derive an explicit formula for solutions of this problem.
Keywords: Cauchy problem, system theory of elasticity, elliptic system, ill-posed problem. 
@article{IVM_2020_4_a4,
     author = {I. E. Niyozov},
     title = {Regularization of a nonstandard {Cauchy} problem for a dynamic {Lame} system},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {54--63},
     publisher = {mathdoc},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_4_a4/}
}
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I. E. Niyozov. Regularization of a nonstandard Cauchy problem for a dynamic Lame system. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2020), pp. 54-63. http://geodesic.mathdoc.fr/item/IVM_2020_4_a4/