Geodesic
Existence of solutions to a self-referred and hereditary system of differential equations
Electronic Journal of Differential Equations, Tome 2006 (2006).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $v(x,0)=v_0(x)$.
Classification : 47J35, 45G10
Keywords: non-linear evolution systems, hereditary systems 
@article{EJDE_2006__2006__a71,
     author = {Pascali, Eduardo},
     title = {Existence of solutions to a self-referred and hereditary system of differential equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2006},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a71/}
}
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Pascali, Eduardo. Existence of solutions to a self-referred and hereditary system of differential equations. Electronic Journal of Differential Equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a71/