Geodesic
Determining of coefficients and the classical solvability of a nonlocal boundary-value problem for the Benney--Luke integro-differential equation with degenerate kernel
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 156 (2018), pp. 89-102

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Using the Fourier method of separation of variables, we examine the classical solvability and construct solutions of a nonlocal inverse boundary-value problem for the fourth-order Benney–Luke integro-differential equation with degenerate kernel. We prove the criterion of the unique solvability of the inverse boundary-value problem and examine the stability of solutions with respect to the recovery function.
Keywords: integro-differential equation, Benney–Luke equation, fourth-order equation, degenerate kernel, integral condition, classical solvability. 
@article{INTO_2018_156_a7,
     author = {T. K. Yuldashev},
     title = {Determining of coefficients and the classical solvability of a nonlocal boundary-value problem for the {Benney--Luke} integro-differential equation with degenerate kernel},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {89--102},
     publisher = {mathdoc},
     volume = {156},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_156_a7/}
}
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T. K. Yuldashev. Determining of coefficients and the classical solvability of a nonlocal boundary-value problem for the Benney--Luke integro-differential equation with degenerate kernel. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 156 (2018), pp. 89-102. http://geodesic.mathdoc.fr/item/INTO_2018_156_a7/