TY  - JOUR
ID  - Zabawa2006
LB  - Zabawa2006
AU  - Zabawa, Tomasz S.
TI  - Stability of solutions of infinite systems of nonlinear differential-functional equations of parabolic type
ST  - Stability of solutions of infinite systems of nonlinear differential-functional equations of parabolic type
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2006
VL  - 26
IS  - 1
SP  - 173
EP  - 183
DO  - http://dx.doi.org/10.7494/OpMath.2006.26.1.173
UR  - http://dx.doi.org/10.7494/OpMath.2006.26.1.173
AB  - A parabolic initial boundary value problem and an associated elliptic Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations are considered. It is shown that the solutions of the parabolic problem is asymptotically stable and the limit of the solution of the parabolic problem as \(t\to\infty\) is the solution of the associated elliptic problem. The result is based on the monotone methods.
KW  - stability of solutions
KW  - infinite systems
KW  - parabolic equations
KW  - elliptic equations
KW  - semilinear differential-functional equations
KW  - monotone iterative method
SN  - 1232-9274
ER  -