TY - JOUR

T1 - Mixed Problem with Integral Condition for a Loaded Third Order Pseudoparabolic Equation

AU - Kozhanov, Alexandr

AU - Zikirov, Obidjan

AU - Kholikov, Dilshod

N1 - The work was supported by the Russian Science Foundation ( project No. 23-21-00269). Публикация для корректировки.

PY - 2023/12

Y1 - 2023/12

N2 - We consider a nonlocal problem with an integral condition for a loaded third order pseudoparabolic equation in a rectangular domain. We prove the unique solvability of the problem with the help of an auxiliary Goursat problem for a pseudoparabolic equation. Based on an integral representation of the solution to the Goursat problem, we reduce the original problem to a Volterra integral equation of the second kind and, using the contraction mapping principle, establish the solvability of the original problem.

AB - We consider a nonlocal problem with an integral condition for a loaded third order pseudoparabolic equation in a rectangular domain. We prove the unique solvability of the problem with the help of an auxiliary Goursat problem for a pseudoparabolic equation. Based on an integral representation of the solution to the Goursat problem, we reduce the original problem to a Volterra integral equation of the second kind and, using the contraction mapping principle, establish the solvability of the original problem.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85180490412&origin=inward&txGid=de513d20ea0344c9c4d57fa50f179e49

UR - https://www.mendeley.com/catalogue/f076676e-9304-304e-bd8f-93d4015f662b/

U2 - 10.1007/s10958-023-06845-9

DO - 10.1007/s10958-023-06845-9

M3 - Article

VL - 277

SP - 420

EP - 430

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

IS - 3

ER -