Geodesic
On the Solvability of Boundary Value Problem for Mixed-type Equation with a Singular Coefficient
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2014), pp. 44-56

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In this paper we study a problem with conditions on the inner characteristic and on some parts of the degeneration line for mixed type equation with singular coefficient in unbounded domain. We prove the uniqueness of solution of the mentioned problem with the help of the extremum principle. The proof of the existence of solution is based on the theory of singular integral equations and Fredholm integral equations.
Keywords: principle of extremum, unique solvability, integral equations, Wiener–Hopf equation, index equation, Fourier integral.
Mots-clés : existence of solution, singular coefficient 
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     author = {M. Kh. Ruziev},
     title = {On the {Solvability} of {Boundary} {Value} {Problem} for {Mixed-type} {Equation} with a {Singular} {Coefficient}},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {44--56},
     publisher = {mathdoc},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2014_3_a3/}
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M. Kh. Ruziev. On the Solvability of Boundary Value Problem for Mixed-type Equation with a Singular Coefficient. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2014), pp. 44-56. http://geodesic.mathdoc.fr/item/VSGTU_2014_3_a3/