Nonlocal problem for an equation of mixed type in a domain whose elliptic part is a half-strip

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 o...

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Bibliographic Details
Published in:Differential equations 2014-06, Vol.50 (6), p.805-814
Main Authors: Repin, O. A., Kumykova, S. K.
Format: Article
Language:English
Subjects:
Boundary value problems
Degeneration
Derivatives
Difference and Functional Equations
Differential equations
Differentiation
Mathematical analysis
Mathematical functions
Mathematical models
Mathematical problems
Mathematics
Mathematics and Statistics
Operators
Ordinary Differential Equations
Partial Differential Equations
Studies
Theorems
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Summary: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.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266114060081