带时滞的退化非线性抛物方程的熄灭

Quenching for a Nonlinear Degenerate Parabolic Equation with Time Delay

该文研究一带时滞的退化非线性抛物方程的初边值问题。运用正则化方法和上下解技巧证明了上述问题的古典正解的局部存在性及其可延拓性。讨论了整体存在性和有限时刻熄灭,建立了临界长度,得到了熄灭点的位置以及特殊f(u)

This paper deals with the initial boundary value problem of a nonlinear degenerate parabolic equation with time delay. The method of regularization and the technique of upper and lower solutions are employed to show the local existence and the continuation of the positive classical solution of the above problem. The global existence and finite time quenching are discussed, and the critical length is established. The location of the quenching points and the estimates of the quenching rate for the special case of $f(u)$ are obtained.