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Differential Equations

, Volume 55, Issue 1, pp 145–148 | Cite as

L2 Solvability of the Tricomi-Neumann Problem for a Parabolic-Hyperbolic Equation with Degenerate Hyperbolic Part

  • N. Yu. KapustinEmail author
Short Communications
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Abstract

We consider the inhomogeneous Tricomi-Neumann problem for a parabolic-hyperbolic equation with noncharacteristic type change line and degenerate hyperbolic part. The auxiliary function method is used to obtain an a priori estimate for the solution. The existence of a classical solution is proved for the case in which the right-hand side of the equation and the boundary functions are smooth. The unique generalized L2 solvability is established for the case of nonsmooth conditions.

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References

  1. 1.
    Kapustin, N.Yu., Solvability in L2 of Tricomi’s problem for a parabolic-hyperbolic equation with a degenerate hyperbolic part, Differ. Equations, 1986, vol. 22, no. 1, pp. 47–51.zbMATHGoogle Scholar
  2. 2.
    Kapustin, N.Yu., L2-solvability of boundary-value problems for equations of mixed type, Differ. Equations, 1989, vol. 25, no. 1, pp. 39–45.zbMATHGoogle Scholar
  3. 3.
    Kapustin, N.Yu., On an inhomogeneous Tricomi problem for a parabolic-hyperbolic equation, Differ. Equations, 2017, vol. 53, no. 10, pp. 1340–1345.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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