Abstract
For the Gellerstedt equation, we study a problem with shift in a domain whose elliptic part is an infinite half-strip. By using generalized fractional differentiation operators, we specify a linear combination that relates the value of the solution on characteristics of the equation with the value of the solution and its derivative on the parabolic degeneration line. We prove the unique solvability of this problem.
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Original Russian Text © O.A. Repin, S.K. Kumykova, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 6, pp. 807–816.
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Repin, O.A., Kumykova, S.K. Nonlocal problem for an equation of mixed type in a domain whose elliptic part is a half-strip. Diff Equat 50, 805–814 (2014). https://doi.org/10.1134/S0012266114060081
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DOI: https://doi.org/10.1134/S0012266114060081