IJPAM: Volume 66, No. 2 (2011)
ONE NONLINEAR PARABOLIC EQUATION
Ilia State University
3/5 Kakutsa Cholokashvili Ave., Tbilisi, 0162, GEORGIA
e-mail: [email protected]
Abstract.In the present paper the difference analogue of the initial-boundary value
problem to one nonlinear parabolic equation is considered. In certain
conditions the convergence of the solution of the difference analogue to the
solution of source problem is proved. For the same difference analogue the
comparison theorem is proved and the uniqueness of the solution is obtained.
The iteration process for finding of the solution of difference analogue is
constructed and in certain conditions its convergence is obtained.
Received: November 4, 2010
AMS Subject Classification: 65M06
Key Words and Phrases: difference analogue, comparison theorem, partial differential equation, convergence
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 2