ISSN: 1813-0410

Author : A. Neamah, Ayat

Homogenuous n-parameters Abstract Cauchy Problem

Ayat A. Neamah

journal of kerbala university, Volume 12, Issue 2, Pages 22-33

We use the semigroup theory to study the homogeneus n-parameter ACP

where X is a Banach space, H_i:D(H_i )⊆X→X ,i=1,2,…,n is a densely – defined closed linear operator. We discuss the existence and uniqueness of solution of n-ACP. In fact, we claim that if (H_1,H_2,… ,H_n) is the generator of a C_0- n parameter semigroup W(t_1,t_2,… ,t_n ) ∶ then n-ACP with some conditions has a unique solution.