Thecritical points and classify them as asymptotically stable or unstable. Also draw the phase line and several graphs of solution in t u 1 − plane of equation d u 1 d t = − ( k 1 + k 2 ) u 1 + k 2 u 20 + k 1 T a , where k 1 , k 2 , u 20 and T a are constants.
Thecritical points and classify them as asymptotically stable or unstable. Also draw the phase line and several graphs of solution in t u 1 − plane of equation d u 1 d t = − ( k 1 + k 2 ) u 1 + k 2 u 20 + k 1 T a , where k 1 , k 2 , u 20 and T a are constants.
Solution Summary: The author determines the critical points and classifies them as asymptotically stable or unstable. They also draw the phase line and several graphs of the solution in tu_1- plane
Thecritical points and classify them as asymptotically stable or unstable. Also draw the phase line and several graphs of solution in tu1− plane of equation du1dt=−(k1+k2)u1+k2u20+k1Ta, where k1,k2,u20andTa are constants.
(b)
To determine
Thesolution of equation du1dt=−(k1+k2)u1+k2u20+k1Ta subject to the initial condition u1(0)=u10, where k1,k2,u20andTa are constants. Use this solution to verify the qualitative result of part (a).
(c)
To determine
Thephysical interpretation of setting ε=0 and the equilibrium solution u1=k2u20+k1Tak1+k2.
(d)
To determine
Thequalitative results implying the sizing of the rock storage pile in combination with temperature that can be achieved in the rock storage pile during the daytime.