The Continuous Dependence On Nonlinearities Of A Singular Diffusion Equations

In this thesis, the continuous dependence on nonlinearities of a singular di?usion equationswith sources is discussed, the existence, asymptotic behavior and the life span of solutions arealso considered.I. Taking a(u) = um(m∈R) and f(u) = aup (a > 0,p > 0) as a model, we discuss thesingular di?usion ut = ?a(u)?f(u) with second initial boundary value is taken over. we provedthat:(1) there exists a unique generalized solution;(2) there exists global generalized solution if and only if p≥1;(3) there exists T1, T2 > 0 such that T1≤T0≤T2, where T0 is the extinguish time of thesolution;(4) the solution approaches to uˉin L2?space as t→∞;(5) the solution u(x,t,m,a) converges to its corresponding solution u(x,t, 1, 0) of the linearequation ut = ?u in L2?space as m→1, a→0, and the explicit error estimate is obtained:II. Considerwhere p, q, a, b > 0, we prove that:(1) the solution (u,v) converges to its corresponding solution of linear equationand the explicit error estimate is obtained; (2) the solution (u,v) converges to its corresponding solution of independent equationand the explicit error estimate is also obtained;(3) the solution of weak-coupling problem (u,v) converges to its average value of space(u,v) in L2?norm when 0 < p,q < 1 as well as t→∞;(4) it prove the global solution about initial value...