奇异抛物型方程最大解的存在性：猝灭现象和瞬时收缩现象
Existence of a maximal solution of singular parabolic equations with absorptions: quenching phenomenon and the instantaneous shrinking phenomenon
摘要：
研究了具有齐次Dirichlet边界条件的一维退化抛物型方程的非负解.为了得到一个存在性结果，我们证明了|u_x|的一个陡梯度估计.此外，我们还研究了非负解的性质，如猝灭现象，有限传播速度等。我们对狄利克雷问题的结果将推广到相应的柯西问题。此外，我们还证明了当f满足一定的增长条件时，非负解的紧支集的瞬时收缩现象。
英文摘要：
This paper deals with nonnegative solutions of the one dimensional degenerate parabolic equations with zero homogeneous Dirichlet boundary condition. To obtain an existence result, we prove a sharp gradient estimate of |u_x|. Besides, we investigate the behaviors of nonnegative solutions such as the quenching phenomenon, and the finite speed of propagation. Our results of the Dirichlet problem will be extended to the associated Cauchy problem. In addition, we show that the phenomenon of the instantaneous shrinking of compact support of the nonnegative solutions occurs if f satisfies some growth condition.
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