$L_2$-estimates for solutions of the general boundary-value problems for the equations with mixed parabolic-elliptic structure

$L_2$-estimates for solutions of the model boundary value problems — Cauchy problem and semispace problem — for linear equation $L\left(\frac\partial{\partial x}, \frac\partial{\partial t}\right)u=0$ in which operator $L$ is product $2b_1$-parabolic operator and $2b_2r$-elliptic operator ($b_1$, $b_2$, $r$ — integer numbers) are obtained.