@inbook{5b26bb5f5f924259b2918330e11872c6,
title = "Ultra-Parabolic Kolmogorov-Type Equation with Multiple Impulsive Sources",
abstract = "Existence and uniqueness of entropy solutions of the Cauchy–Dirichlet problem for the non-autonomous ultra-parabolic equation with partial diffusivity and multiple impulsive sources is established. The limiting passage from the equation incorporating a single distributed source to the multi-impulsive equation is fulfilled, as the distributed source collapses to a parameterized multi-atomic Dirac delta measure.",
keywords = "Entropy solution, Impulsive source, Ultra-parabolic equation",
author = "Ivan Kuznetsov and Sergey Sazhenkov",
note = "Funding Information: The work was supported by the Ministry of Science and Higher Education of the Russian Federation (project no. III.22.4.2) and by the Russian Foundation for Basic Research (grant no. 18-01-00649). The authors are very grateful to Professor Stanislav N. Antontsev (CMAFCIO, Universidade de Lisboa, Portugal) for fruitful discussions and to the supervisors of the session {\textquoteleft}Partial Differential Equations with Nonstandard Growth{\textquoteright} at the 12th International ISAAC Congress held in Aveiro in 2019, Professor Hermenegildo Borges de Oliveira (University of Algarve, Faro, Portugal) and Professor Sergey I. Shmarev (University of Oviedo, Spain) for kind invitation to take part in the session and for fruitful discussions. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
year = "2022",
doi = "10.1007/978-3-030-87502-2_57",
language = "English",
series = "Trends in Mathematics",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "565--574",
booktitle = "Trends in Mathematics",
address = "Germany",
}