On behavior of solutions of the quasilinear second-order parabolic equations in unbounded noncylindrical domains
- 33 Downloads
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.
KeywordsParabolic Equation Special Kind Initial Boundary Noncylindrical Domain Mixed Initial Boundary
Unable to display preview. Download preview PDF.
- 1.A. E. Shishkov, “The classes of uniqueness of the solutions to mixed problems for parabolic equation in noncylindrical domains,”Dokl. Akad. Nauk. Ukr. SSR, Ser. A, No. 11, 35–37 (1988).Google Scholar
- 2.E. M. Landis,Second Order Equations of Elliptic and Parabolic Types [in Russian], Nauka, Moscow (1971).Google Scholar
- 3.O. A. Oleinik and E. V. Radkevich,Second Order Equations with Nonnegative Characteristic Forms, VINITI Series in Mathematics (1971) [in Russian], VINITI, Moscow (1971).Google Scholar
- 4.O. A. Oleinik and E. V. Radkevich, “The method of introducing a parameter for the investigation of evolutionary equations,”Usp. Mat. Nauk,33, Issue 5, 7–76 (1978).Google Scholar
- 5.A. N. Tikhonov, “Theorems of uniqueness for heat conduction equations,”Mat. Sb.,42, No. 2, 199–215 (1935).Google Scholar
- 6.J. Hwang, “Comparison Principles and Liouville Theorems for Prescribed Mean Curvature Equations in Unbounded Domains,”An. Scuola Norm. Sup. Pisa, Ser. 4,15, No. 3, 341–355 (1988).Google Scholar