Geodesic
The Second Boundary-Value Problem for Pseudoparabolic Equations in Noncylindrical Domains
Matematičeskie zametki, Tome 72 (2002) no. 1, pp. 48-53.

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This paper is devoted to the study of the solvability of the second mixed problem in a noncylindrical domain for the nonstationary equation $$ \operatorname {div}(k(x)\operatorname {grad}u_t)-c(x)u_t-b(x)u(x,t)=f(x,t), $$ called the pseudoparabolic equation. We prove existence and uniqueness theorems for the solution in the case of contracting (as time $t$ increases) domains. 
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M. V. Ivanova; V. I. Ushakov. The Second Boundary-Value Problem for Pseudoparabolic Equations in Noncylindrical Domains. Matematičeskie zametki, Tome 72 (2002) no. 1, pp. 48-53. http://geodesic.mathdoc.fr/item/MZM_2002_72_1_a4/

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