Geodesic
On the well-posedness of Cauchy problems for nonstationary equations with the unselected highest time derivative and the definition of the trace of distribution on the hyperplane of the initial data
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 2, Tome 191 (2021), pp. 47-73

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In this paper, we examine the well-posedness of Cauchy problems for nonstationary partial differential equations with nonselected highest time derivatives that have degeneration by these derivatives. For this purpose, we introduce the notion of the trace on the initial data hyperplane for distributions with semi-bounded supports, which allows one to establish some properties of the solution that ensure the well-posedness of the problems considered.
Keywords: nonstationary equation, unselected highest derivative, Cauchy problem, nonuniqueness, solution focusing, well-posedness, restriction, trace of distribution. 
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     author = {Yu. V. Zasorin},
     title = {On the well-posedness of {Cauchy} problems for nonstationary equations with the unselected highest time derivative and the definition of the trace of distribution on the hyperplane of the initial data},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {47--73},
     publisher = {mathdoc},
     volume = {191},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_191_a5/}
}
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Yu. V. Zasorin. On the well-posedness of Cauchy problems for nonstationary equations with the unselected highest time derivative and the definition of the trace of distribution on the hyperplane of the initial data. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 2, Tome 191 (2021), pp. 47-73. http://geodesic.mathdoc.fr/item/INTO_2021_191_a5/