The qualitative analysis of a dynamical system modeling the formation of two-layer scales on pure metals

R. L. Baker
1995 Proceedings of the American Mathematical Society  
F. Gesmundo and F. Viani have modeled the growth rates of twooxide scales by the system: We provide a complete qualitative analysis of (1.1) by making use of known results about the general «-dimensional dynamical system: We show that for m > 1 , the Gesmundo-Viani system admits a unique parabolic solution qi(t) = c¡yft, c, > 0. This parabolic solution attracts all other solutions. Every solution extends uniquely to a solution on [0, +oo), such that the extended solution is eventually
more » ... lly increasing. Finally, the trajectory of any solution coincides with a trajectory of the following linear system: dqx m-\ K2 K2 dq2 K2 Kx -j7-=-í<¡i+m^-q2, -f± = -^qx+m-¿q2. dt m 2 2 dt 2 2
doi:10.1090/s0002-9939-1995-1264803-4 fatcat:hdwqfmnvwrhzdl6iigjsu2avfm