In this paper, we study the behavior in time of the solutions for a class of parabolic problems including the p-Laplacian equation and the heat equation. Either the case of singular or degenerate equations is considered. The initial datum \(u_0\) is a summable function and a reaction term f is present in the problem. We prove that, despite the lack of regularity of \(u_0\), immediate regularization of the solutions appears for data f sufficiently regular and we derive estimates that for zero data f become the known decay estimates for these kinds of problems. Besides, even if f is not regular, we show that it is possible to describe the behavior in time of a suitable class of solutions. Finally, we establish some uniqueness results for the solutions of these evolution problems.

在本文中，我们研究了一类抛物线问题（包括p -Laplacian方程和热方程）的解的时间行为。考虑奇异方程或简并方程的情况。初始数据\（u_0 \）是一个可加函数，并且反应项f存在于问题中。我们证明，尽管缺乏\（u_0 \）的正则性，但对于数据f而言，足够规则的解出现了立即正则化，并且我们推导出了对于零数据f的估计成为此类问题的已知衰减估计。此外，即使f这是不规则的，我们证明有可能及时描述适当类别的解决方案的行为。最后，我们为解决这些演化问题建立了一些唯一性结果。