Electron. J. Diff. Eqns., Vol. 2006(2006), No. 07, pp. 1-7.

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

Eduardo Pascali

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.

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Eduardo Pascali
Department of Mathematics ''Ennio De Giorgi'', University of Lecce, C. P. 193, 73100, Lecce, Italy
email: eduardo.pascali@unile.it

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