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
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.
Kapustin, N.Yu., L2-solvability of boundary-value problems for equations of mixed type, Differ. Equations, 1989, vol. 25, no. 1, pp. 39–45.
Kapustin, N.Yu., On an inhomogeneous Tricomi problem for a parabolic-hyperbolic equation, Differ. Equations, 2017, vol. 53, no. 10, pp. 1340–1345.
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Russian Text © N.Yu. Kapustin, 2019, published in Differentsial’nye Uravneniya, 2019, Vol. 55, No. 1, pp. 141–144.
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Kapustin, N.Y. L2 Solvability of the Tricomi-Neumann Problem for a Parabolic-Hyperbolic Equation with Degenerate Hyperbolic Part. Diff Equat 55, 145–148 (2019). https://doi.org/10.1134/S0012266119010166
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DOI: https://doi.org/10.1134/S0012266119010166