The behavior of the solution of a mixed problem for the Sobolev equation in a cylindrical domain as \(t\rightarrow +\infty\) (Q1395212)

The author considers a mixed problem for the Sobolev equation \( \frac{d^2\Delta{u}}{dt^2}+\frac{d^2u}{dx_1^2}=0\) in a cylindrical domain as \(t\rightarrow+\infty\). Note that the mixed problem for equations in which the operator at the higher time derivative does not have real zeros (the nonsingular case) have been studied earlier. Except for the Cauchy problem and the mixed problem in a quadrant, the singular case has not been studied yet. In the present work, the singular case is studied.