Geodesic
A problem with nonlocal integral 1st kind conditions for 4th order partial differential equation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 30 (2024) no. 2, pp. 30-44

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In this article, we consider a nonlocal problem with integral conditions for one-dimensional 4th order partial differential equation. A distinguishing feature of this problem is the presence of integral conditions of the 1st kind. Moreover, the kernels of these conditions depend on both spatial and time variables. We suggest a new approach which enables to overcome the difficulties arising from the form of nonlocal conditions and derive a priori estimates. Obtained estimates play a significant role when we prove the existence and uniqueness of the solution to the problem.
Keywords: 4th-order partial differential equation, nonlocal problem, integral conditions of 1st and 2nd kind, generalized solution, Sobolev space, a priori estimates. 
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     author = {L. S. Pulkina},
     title = {A problem with nonlocal integral 1st kind conditions for 4th order partial differential equation},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {30--44},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2024_30_2_a3/}
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L. S. Pulkina. A problem with nonlocal integral 1st kind conditions for 4th order partial differential equation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 30 (2024) no. 2, pp. 30-44. http://geodesic.mathdoc.fr/item/VSGU_2024_30_2_a3/