This paper studies the large-time behavior of solutions to the quasilinear inhomogeneous parabolic equation with combined nonlinearities. This equation is a natural extension of the heat equations with combined nonlinearities considered by Jleli et al. (Proc Am Math Soc 148:2579–2593, 2020). Firstly, we focus on an interesting phenomenon of discontinuity of the critical exponents. In particular, we will fill the gap in the results of Jleli et al. (2020) for the critical case. We are also interested in the influence of the forcing term on the critical behavior of the considered problem, so we will define another critical exponent depending on the forcing term.

本文研究了具有组合非线性的拟线性非齐次抛物型方程解的大时间行为。该方程是 Jleli 等人考虑的具有组合非线性的热方程的自然延伸。（Proc Am Math Soc 148：2579–2593，2020）。首先，我们关注一个有趣的临界指数不连续现象。特别是，我们将填补 Jleli 等人研究结果的空白。（2020）对于关键案例。我们还对强迫项对所考虑问题的关键行为的影响感兴趣，因此我们将根据强迫项定义另一个关键指数。