We consider the Fourier first initial-boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations of parabolic type. The right-hand sides of the system are functionals of unknown functions. The existence and uniqueness of the solution are proved by the Banach fixed point theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap77-1-1,
author = {Stanis\l aw Brzychczy},
title = {Existence and uniqueness of solutions of nonlinear infinite systems of parabolic differential-functional equations},
journal = {Annales Polonici Mathematici},
volume = {77},
year = {2001},
pages = {1-9},
zbl = {0985.35099},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap77-1-1}
}
Stanisław Brzychczy. Existence and uniqueness of solutions of nonlinear infinite systems of parabolic differential-functional equations. Annales Polonici Mathematici, Tome 77 (2001) pp. 1-9. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap77-1-1/