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Ultra-Parabolic Kolmogorov-Type Equation with Multiple Impulsive Sources

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Current Trends in Analysis, its Applications and Computation

Part of the book series: Trends in Mathematics ((RESPERSP))

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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.

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References

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Acknowledgements

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.

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Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russia

    Ivan Kuznetsov & Sergey Sazhenkov

  2. Novosibirsk State University, Novosibirsk, Russia

    Ivan Kuznetsov & Sergey Sazhenkov

Authors
  1. Ivan Kuznetsov
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  2. Sergey Sazhenkov
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Editors and Affiliations

  1. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Paula Cerejeiras

  2. Institut of Applied Analysis, TU Bergakademie Freiberg, Freiberg, Germany

    Michael Reissig

  3. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Irene Sabadini

  4. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Joachim Toft

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Kuznetsov, I., Sazhenkov, S. (2022). Ultra-Parabolic Kolmogorov-Type Equation with Multiple Impulsive Sources. In: Cerejeiras, P., Reissig, M., Sabadini, I., Toft, J. (eds) Current Trends in Analysis, its Applications and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-87502-2_57

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