Comparison theorems for infinite systems of parabolic functional-differential equations

Danuta Jaruszewska-Walczak. "Comparison theorems for infinite systems of parabolic functional-differential equations." Annales Polonici Mathematici 77.3 (2001): 261-270. <http://eudml.org/doc/280502>.

@article{DanutaJaruszewska2001,
abstract = {The paper deals with a weakly coupled system of functional-differential equations $∂_t u_i(t,x) = f_i(t,x,u(t,x),u,∂_x u_i(t,x),∂_\{xx\}u_i(t,x))$, i ∈ S, where (t,x) = (t,x₁,...,xₙ) ∈ (0,a) × G, $u = \{u_i\}_\{i∈S\}$ and S is an arbitrary set of indices. Initial boundary conditions are considered and the following questions are discussed: estimates of solutions, criteria of uniqueness, continuous dependence of solutions on given functions. The right hand sides of the equations satisfy nonlinear estimates of the Perron type with respect to the unknown functions. The results are based on a theorem on extremal solutions of an initial problem for infinite systems of ordinary functional-differential equations.},
author = {Danuta Jaruszewska-Walczak},
journal = {Annales Polonici Mathematici},
keywords = {nonlinear estimates of the Perron type; estimates of solutions; uniqueness; continuous dependence},
language = {eng},
number = {3},
pages = {261-270},
title = {Comparison theorems for infinite systems of parabolic functional-differential equations},
url = {http://eudml.org/doc/280502},
volume = {77},
year = {2001},
}

TY - JOUR
AU - Danuta Jaruszewska-Walczak
TI - Comparison theorems for infinite systems of parabolic functional-differential equations
JO - Annales Polonici Mathematici
PY - 2001
VL - 77
IS - 3
SP - 261
EP - 270
AB - The paper deals with a weakly coupled system of functional-differential equations $∂_t u_i(t,x) = f_i(t,x,u(t,x),u,∂_x u_i(t,x),∂_{xx}u_i(t,x))$, i ∈ S, where (t,x) = (t,x₁,...,xₙ) ∈ (0,a) × G, $u = {u_i}_{i∈S}$ and S is an arbitrary set of indices. Initial boundary conditions are considered and the following questions are discussed: estimates of solutions, criteria of uniqueness, continuous dependence of solutions on given functions. The right hand sides of the equations satisfy nonlinear estimates of the Perron type with respect to the unknown functions. The results are based on a theorem on extremal solutions of an initial problem for infinite systems of ordinary functional-differential equations.
LA - eng
KW - nonlinear estimates of the Perron type; estimates of solutions; uniqueness; continuous dependence
UR - http://eudml.org/doc/280502
ER -