The Qualitative Properties On A Parabolic System With Sources

In this paper, some qualitative questions of a quasilinear parabolic equations with sources are discussed, such as the existence, asymptotic behavior, the life span of solutions and so on.I. The singular diffusion ut=m/1uxx+αup with second initial boundary value is consid-ered. it proved that:(1) the existence of global smooth solution;(2) the estimated of blow-up time;(3) the asymptotic properties as tâ†'∞;(4) the solutions u(x, t, m, a) converge to their corresponding solution u(x, t,1,0) of the linear equation ut=uxx in L2-as mâ†'1, αâ†'0, and the explicit error estimate is obtained:II. Consider where0<p, q<1, we prove that:(1) the existence of solutions of the cauchy problem;(2) the solution (u, v) converges to its corresponding solution of independent equation the continuous dependence on initial of the solution is proved, the explicit error estimate is also obtained:...