On the solvability of a nonlocal problem arising in dynamics of moisture transfer.

*(English)*Zbl 1059.35072Summary: In the recent years, evolution problems with an integral term in the boundary conditions have received a great deal of attention. Such problems, in general, are nonself-adjoint, and this poses the basic source of difficulty, which can considerably complicate the application of standard functional and numerical techniques. To avoid these complications, we have introduced a nonclassical function space to establish a priori estimates without any additional complication as compared to the classical evolution problems. As an example of the applicability of this way of solving problems of this type, we investigate an initial-boundary value problem for a pseudoparabolic equation which combines Neumann and integral conditions.

##### MSC:

35K70 | Ultraparabolic equations, pseudoparabolic equations, etc. |

35D05 | Existence of generalized solutions of PDE (MSC2000) |

35B45 | A priori estimates in context of PDEs |

35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |

35S05 | Pseudodifferential operators as generalizations of partial differential operators |