Opuscula Math. 32, no. 3 (2012), 529-549
http://dx.doi.org/10.7494/OpMath.2012.32.3.529
Opuscula Mathematica
Estimates of solutions for parabolic differential and difference functional equations and applications
Abstract. The theorems on the estimates of solutions for nonlinear second-order partial differential functional equations of parabolic type with Dirichlet's condition and for suitable implicit finite difference functional schemes are proved. The proofs are based on the comparison technique. The convergent and stable difference method is considered without the assumption of the global generalized Perron condition posed on the functional variable but with the local one only. It is a consequence of our estimates theorems. In particular, these results cover quasi-linear equations. However, such equations are also treated separately. The functional dependence is of the Volterra type.
Keywords: parabolic differential and discrete functional equations, estimate of solution, implicit difference method.
Mathematics Subject Classification: 35R10, 35B30, 65M12, 65M06.
- Lucjan Sapa
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland
- Received: 2010-11-15.
- Revised: 2011-09-01.
- Accepted: 2011-09-13.
