Existence of solutions to a self-referred and hereditary system of differential equations
Texas State University-San Marcos, Department of Mathematics
We establish the existence and uniqueness of a local solution for the system of differential equations ∂/∂t u(x, t) = u(v(∫t0 u(x, s)ds, t), t) ∂/∂t v(x, t) = v(u(∫t0 v(x, s)ds, t), t). with given initial conditions u(x, 0) = u0(x) and v(x, 0) = v0(x).
Non-linear evolution systems, Hereditary systems
Pascali, E. (2006). Existence of solutions to a self-referred and hereditary system of differential equations. <i>Electronic Journal of Differential Equations, 2006</i>(07), pp. 1-7.