Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 07, pp. 1-7.
Title: Existence of solutions to a self-referred and hereditary
system of differential equations
Author: Eduardo Pascali (Univ. of Lecce, Italy)
Abstract:
We establish the existence and uniqueness of a local solution
for the system of differential equations
$$\displaylines{
\frac{\partial }{\partial t}u(x,t)
= u\Big(v\Big(\int_0^t u(x,s)ds, t\Big), t\Big) \cr
\frac{\partial }{\partial t}v(x,t)
= v\Big(u\Big(\int_0^t v(x,s)ds, t\Big), t\Big).
}$$
with given initial conditions $u(x,0)=u_0(x)$ and $v(x,0)=v_0(x)$.
Submitted June 13, 2005. Published January 16, 2006.
Math Subject Classifications: 47J35, 45G10.
Key Words: Non-linear evolution systems; Hereditary systems.