14 12. THE THEOREM OF PICARD-LINDELOEF The system below is used for the description of chemical oscillators like the Belousov-Zhabotinsky reaction. It is known as Brusselator in the literature. Let ki, k2, k3, k > 0 be positive real numbers and let A, B > 0 be positive real numbers. Consider for an unknown function u:ICR2 with components u(t) = ((t), y(t)) the IVP (c(t) = k1A k2B - r(t) + kz-(t)?y(t) - k4. f(t), y(t) = k B . (t) k3.0(t)?y(t), (0) = to, y(0) = yo. where co >0 and yo > 0. (1) Please classify the above ODE. (2) Please show that there exists a positive time T >0 and a unique continously differentiable solution u : 0,T) + R2 to the above IVP. 14 12. THE THEOREM OF PICARD-LINDELOEF The system below is used for the description of chemical oscillators like the Belousov-Zhabotinsky reaction. It is known as Brusselator in the literature. Let ki, k2, k3, k > 0 be positive real numbers and let A, B > 0 be positive real numbers. Consider for an unknown function u:ICR2 with components u(t) = ((t), y(t)) the IVP (c(t) = k1A k2B - r(t) + kz-(t)?y(t) - k4. f(t), y(t) = k B . (t) k3.0(t)?y(t), (0) = to, y(0) = yo. where co >0 and yo > 0. (1) Please classify the above ODE. (2) Please show that there exists a positive time T >0 and a unique continously differentiable solution u : 0,T) + R2 to the above IVP