TY  - JOUR
ID  - Sapa2012
LB  - Sapa2012
AU  - Sapa, Lucjan
TI  - Estimates of solutions for parabolic differential and difference functional equations and applications
ST  - Estimates of solutions for parabolic differential and difference functional equations and applications
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2012
VL  - 32
IS  - 3
SP  - 529
EP  - 549
DO  - http://dx.doi.org/10.7494/OpMath.2012.32.3.529
UR  - http://dx.doi.org/10.7494/OpMath.2012.32.3.529
AB  - 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.
KW  - parabolic differential and discrete functional equations
KW  - estimate of solution
KW  - implicit difference method
SN  - 1232-9274
ER  -