On decay rate of solution to degenerating linear parabolic equations

Existence and uniqueness of the solution to a linear degenerating parabolic equation is established in unbounded domains by the method of Galerkin's approximations. The first and the third boundary-value conditions are considered. The upper estimate of the solution decay rate is established when $x\to\infty$ in view of the influence of higher-order coefficients of the equation. The upper estimate of the decay rate of the solution $t\to\infty$ depending on the geometry of the unbounded domain is proved as well.