一类含参数非线性抛物型方程的熄灭问题

THE QUENCHING PROBLEM FOR NONLINEAR PARABOLIC EQUATION WITH PARAMETERS

本文讨论了问题的解的“熄灭”现象,主要结果有: (1)对不同的λ>0,求出了ι_o(λ)和ι_1(λ),当ι<ι_o(λ)时解全局存在,当ι>ι_1(λ)时解熄灭:并指出存在ι~·(λ),ι_ο(λ)<ι~·(λ)<ι_1(λ),当ι<ι~·(λ)时解全局存在.当ι>ι~·(λ)时解熄灭。 (2)ι~·(λ)当0<λ<+∞时连续,且可看出,它是λ的减函数。 (3)处不连续.

We discuss the`Quenching＇of a solution for the equation. The main results are the following: (1)For the different λ>O, we find l_o(λ) and l_1(λ), when l< l_o(λ), the solution exists globally and when 1>1_1(λ), the quenching of the solution occurs. Moreover, there exists l~*(λ)such that l_o(λ)<l~*(λ)<l_1(λ)when l<l~*(λ), or l>l~*(λ)the solution exists globally or quenches respectively. (2)For O<λ<+∞, l*(λ)will be continuous and it can be seen that 1~*(λ)will be a dccreasing function. (3)Lim 1~*(λ)=O and l~*(λ)will be discontinuous at λ=O.