On behavior of solutions of the quasilinear second-order parabolic equations in unbounded noncylindrical domains

The theorems of uniqueness of solutions are formulated in the classes of increasing functions for a mixed initial boundary value problem for the second-order degenerate quasiparabolic equations in unbounded noncylindrical domains. We presenta priori estimates of a special kind, analogous to the Saint-Venant principle. The proofs are based on the method of introducing a parameter.Translated from Ukrainskii Matematicheskii Zhumal, Vol. 45, No. 4, pp. 492–499, April, 1993.