We considered the Cauchy problem of a class of quasilinear parabolic equations with strong absorption terms.Due to the effect of the strong absorption term,the solution to the problem could possess compact support and extinguish at a finite time.Firstly,by using the comparison principle and constructing suitable supersolutions,it was proven that the solution possessed a uniform compact support after a certain time and even after any positive time.Secondly,under some conditions,it was proven that the solution extinguished at a finite time by using the L1 norm estimates of the solution to the problem at different times.
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