Existence of solutions for infinite systems of parabolic equations with functional dependence
Volume 86 / 2005
Annales Polonici Mathematici 86 (2005), 123-135
MSC: Primary 35K15; Secondary 35K55, 35R10, 47H10.
DOI: 10.4064/ap86-2-3
Abstract
The Cauchy problem for an infinite system of parabolic type equations is studied. General operators of parabolic type of second order with variable coefficients are considered and the system is weakly coupled. We prove the existence and uniqueness of a bounded solution under Carathéodory type conditions and its differentiability, as well as the existence and uniqueness in the class of functions satisfying a natural growth condition. Both results are obtained by the fixed point method.
