Geodesic
The nonlocal problem for a non-stationary third order composite type equation with general boundary condition
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 1, pp. 187-198

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We consider a nonlocal boundary value problem for non-stationary composite type equation of the third order. The values of function and its derivatives up to the second order on the boundary are given as a linear combination. The initial conditions are nonlocal. We prove the unique solvability for this problem. In proving the problem solution uniqueness we use the method of energy integrals and the theory of quadratic forms. For the problem solution construction we use the potential theory and Volterra integral equations. Some asymptotic properties of the fundamental solutions of the equation are studied.
Keywords: non-stationary equations, fundamental solutions, boundary value problem, potential theory, energy integral method, third order equations, system of integral equations, nonlocal problem.
Mots-clés : composite type equations 
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     author = {A. R. Khashimov},
     title = {The nonlocal problem for a non-stationary third order composite type equation with general boundary condition},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {187--198},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2020_24_1_a10/}
}
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A. R. Khashimov. The nonlocal problem for a non-stationary third order composite type equation with general boundary condition. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 1, pp. 187-198. http://geodesic.mathdoc.fr/item/VSGTU_2020_24_1_a10/