Abstract: In this paper, we investigate a class of second-order nonlinear parabolic equations. Under some conditions about the nonlinear source term, we obtain the quenching phenomena of the Cauchy problem. It is shown that, with more generally nonlinear absorption, the solution quenches in finite time under some restrictions on the exponents of the source term and the initial data. When the structure of the nonlinear absorption is changed, the solution of the Cauchy problem for the second-order nonlinear parabolic equation may exist globally. In the end, we illustrate the behavior of quenching phenomena through simulation experiments. The larger the source term exponents are, the shorter the quenching time is. Our main tools are the comparison principle, the maximum principle and the eigenfunction method.

Key words: parabolic equation, nonlinear source term, quenching phenomena, unbounded domain