Existence of solutions to a self-referred and hereditary system of differential equations

Abstract

We establish the existence and uniqueness of a local solution for the system of differential equations $$displaylines{ frac{partial }{partial t}u(x,t) = uBig(vBig(int_0^t u(x,s)ds, tBig), tBig) cr frac{partial }{partial t}v(x,t) = vBig(uBig(int_0^t v(x,s)ds, tBig), tBig). }$$ with given initial conditions $u(x,0)=u_0(x)$ and $v(x,0)=v_0(x)$.

Keywords

• Non-linear evolution systems
• Hereditary systems.