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Solution of a Semi-Boundary-Value Problem for a First-Order Degenerate Partial Differential Equation

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Abstract

A first-order partial differential equation with constant irreversible coefficients in a Banach space is considered. In the particular case of a finite-dimensional space, the initial-boundary-value problem with irreversible matrix coefficients has no solution; hence, we pose Showalter-type conditions. Due to the regularity of the operator pencil, the equation splits into differential equations in subspaces and given conditions lead to initial conditions in subspaces. A solution to the problem is constructed and an example is provided.

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Authors and Affiliations

  1. Voronezh State University, Voronezh, Russia

    S. P. Zubova & M. A. Hosni

  2. G. F. Morozov Voronezh State University of Forestry and Technologies, Voronezh, Russia

    V. I. Uskov

Authors
  1. S. P. Zubova
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  2. M. A. Hosni
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  3. V. I. Uskov
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Correspondence to S. P. Zubova.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 172, Proceedings of the Voronezh Winter Mathematical School “Modern Methods of Function Theory and Related Problems,” Voronezh, January 28 – February 2, 2019. Part 3, 2019.

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Zubova, S.P., Hosni, M.A. & Uskov, V.I. Solution of a Semi-Boundary-Value Problem for a First-Order Degenerate Partial Differential Equation. J Math Sci 268, 46–55 (2022). https://doi.org/10.1007/s10958-022-06178-z

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  • DOI: https://doi.org/10.1007/s10958-022-06178-z

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