Geodesic
Existence of a solution to the Cauchy problem for the aggregation equation in hyperbolic space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2020), pp. 33-44

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In hyperbolic space, we consider the Cauchy problem for the aggregation equation. Non-negative initial function limited and summable. The existence of a weak solution is proved on small time interval. In the case where the kernel of the integral operator is smooth and rapidly decreases at infinity, the existence of a bounded solution on an arbitrary interval of time is proved.
Keywords: the aggregation equation, hyperbolic space.
Mots-clés : solution existence 
@article{IVM_2020_7_a3,
     author = {V. F. Vil'danova},
     title = {Existence of a solution to the {Cauchy} problem for the aggregation equation in  hyperbolic space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {33--44},
     publisher = {mathdoc},
     number = {7},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_7_a3/}
}
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V. F. Vil'danova. Existence of a solution to the Cauchy problem for the aggregation equation in  hyperbolic space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2020), pp. 33-44. http://geodesic.mathdoc.fr/item/IVM_2020_7_a3/