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Existence of Weak Solutions of Aggregation Integro-Differential Equations

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Abstract

In this work, we investigate the mixed problem for anisotropic integro-differential equations with variable nonlinearity indices. Using the digitization method with respect to time, we prove the existence of a weak solution in a bounded cylinder. We provide a lifetime estimate for the solution.

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Author information

Authors and Affiliations

  1. Bashkir State Pedagogical University, Ufa, Russia

    V. F. Vildanova

  2. Institute of Mathematics with Computer Center of the RAS, Ufa, Russia

    F. Kh. Mukminov

  3. Ufa State Aviation Technical University, Ufa, Russia

    F. Kh. Mukminov

Authors
  1. V. F. Vildanova
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  2. F. Kh. Mukminov
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Corresponding author

Correspondence to V. F. Vildanova.

Additional information

Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 63, No. 4, Differential and Functional Differential Equations, 2017.

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Vildanova, V.F., Mukminov, F.K. Existence of Weak Solutions of Aggregation Integro-Differential Equations. J Math Sci 259, 775–790 (2021). https://doi.org/10.1007/s10958-021-05661-3

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  • DOI: https://doi.org/10.1007/s10958-021-05661-3

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