Geodesic
On a nonlocal boundary-value problem for a loaded parabolic-hyperbolic equation with three lines of degeneracy
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 25 (2021) no. 3, pp. 407-422

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The work is devoted to the proof of the uniqueness and existence of a solution of a nonlocal problem for a loaded parabolic-hyperbolic equation with three lines of change of type. Using the representation of the general solution, the uniqueness of the solution is proved, and the existence of the solution is proved by the method of integral equations. Necessary conditions for the parameters and specified functions are established for the unique solvability of Volterra integral equations of the second kind with a shift equivalent to the problem under study.
Keywords: loaded equation, nonlocal problem, Volterra integral equation with a shift, Green's function, uniqueness and existence of a solution. 
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     author = {B. I. Islomov and J. A. Xolbekov},
     title = {On a nonlocal boundary-value problem for a loaded parabolic-hyperbolic equation with three lines of degeneracy},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
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B. I. Islomov; J. A. Xolbekov. On a nonlocal boundary-value problem for a loaded parabolic-hyperbolic equation with three lines of degeneracy. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 25 (2021) no. 3, pp. 407-422. http://geodesic.mathdoc.fr/item/VSGTU_2021_25_3_a0/