Kurta V. V.
On behavior of solutions of the quasilinear second-order parabolic equations in unbounded noncylindrical domains
Ukr. Mat. Zh. - 1993. - 45, № 4. - pp. 492–499
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.
Ukr. Mat. Zh. - 1992. - 44, № 2. - pp. 279–283
Analogues of the well known in the theory of analytic functions Phragmén-Lindelöff theorem are formulated for the solutions of a wide class of quasilinear equations of elliptic type. Examples are given which illustrate the sharpness of the obtained results for solutions of equations of the form div(|∇u|α−2∇u)=f(x, u), where the function f(x, u) is locally bounded in IRn+1,f(x, 0)=0,uf(x, u)⩾a¦u¦1+q,a>0,α>1,α-1>q⩾0, n⩾2.