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Ultra-Parabolic Kolmogorov-Type Equation with Multiple Impulsive Sources. / Kuznetsov, Ivan; Sazhenkov, Sergey.

Current Trends in Analysis, its Applications and Computation. ред. / Paula Cerejeiras; Michael Reissig; Irene Sabadini; Joachim Toft. 1. ред. Springer Science and Business Media Deutschland GmbH, 2022. стр. 565-574 57 (Trends in Mathematics).

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Harvard

Kuznetsov, I & Sazhenkov, S 2022, Ultra-Parabolic Kolmogorov-Type Equation with Multiple Impulsive Sources. в P Cerejeiras, M Reissig, I Sabadini & J Toft (ред.), Current Trends in Analysis, its Applications and Computation. 1 изд., 57, Trends in Mathematics, Springer Science and Business Media Deutschland GmbH, стр. 565-574. https://doi.org/10.1007/978-3-030-87502-2_57

APA

Kuznetsov, I., & Sazhenkov, S. (2022). Ultra-Parabolic Kolmogorov-Type Equation with Multiple Impulsive Sources. в P. Cerejeiras, M. Reissig, I. Sabadini, & J. Toft (Ред.), Current Trends in Analysis, its Applications and Computation (1 ред., стр. 565-574). [57] (Trends in Mathematics). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-87502-2_57

Vancouver

Kuznetsov I, Sazhenkov S. Ultra-Parabolic Kolmogorov-Type Equation with Multiple Impulsive Sources. в Cerejeiras P, Reissig M, Sabadini I, Toft J, Редакторы, Current Trends in Analysis, its Applications and Computation. 1 ред. Springer Science and Business Media Deutschland GmbH. 2022. стр. 565-574. 57. (Trends in Mathematics). doi: 10.1007/978-3-030-87502-2_57

Author

Kuznetsov, Ivan ; Sazhenkov, Sergey. / Ultra-Parabolic Kolmogorov-Type Equation with Multiple Impulsive Sources. Current Trends in Analysis, its Applications and Computation. Редактор / Paula Cerejeiras ; Michael Reissig ; Irene Sabadini ; Joachim Toft. 1. ред. Springer Science and Business Media Deutschland GmbH, 2022. стр. 565-574 (Trends in Mathematics).

BibTeX

@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",
isbn = "978-3-030-87501-5",
series = "Trends in Mathematics",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "565--574",
editor = "Paula Cerejeiras and Michael Reissig and Irene Sabadini and Joachim Toft",
booktitle = "Current Trends in Analysis, its Applications and Computation",
address = "Germany",
edition = "1",

}

RIS

TY - CHAP

T1 - Ultra-Parabolic Kolmogorov-Type Equation with Multiple Impulsive Sources

AU - Kuznetsov, Ivan

AU - Sazhenkov, Sergey

N1 - 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 ‘Partial Differential Equations with Nonstandard Growth’ 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: © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Entropy solution

KW - Impulsive source

KW - Ultra-parabolic equation

UR - http://www.scopus.com/inward/record.url?scp=85139513091&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/42628365-3032-3c7f-9133-7b9b00c557c3/

U2 - 10.1007/978-3-030-87502-2_57

DO - 10.1007/978-3-030-87502-2_57

M3 - Chapter

AN - SCOPUS:85139513091

SN - 978-3-030-87501-5

T3 - Trends in Mathematics

SP - 565

EP - 574

BT - Current Trends in Analysis, its Applications and Computation

A2 - Cerejeiras, Paula

A2 - Reissig, Michael

A2 - Sabadini, Irene

A2 - Toft, Joachim

PB - Springer Science and Business Media Deutschland GmbH

ER -

ID: 38151653