Assuming

,

u 0 ∈ L 1 ⁢ ( ℝ N ) ∩ L ∞ ⁢ ( ℝ N ) ∩ C ⁢ ( ℝ N ) {u_{0}\in L^{1}(\mathbb{R}^{N})\cap L^{\infty}(\mathbb{R}^{N})\cap C(\mathbb{R% }^{N})}

,

m > 1 {m>1}

,

p > 1 {p>1}

, and

m ⁢ ( p - 1 ) > 1 {m(p-1)>1}

, we prove that

u q {u_{q}}

converges in

C ⁢ ( [ τ , T ] ; L 1 ⁢ ( ℝ N ) ) {C([\tau,T];L^{1}(\mathbb{R}^{N}))}

, for every

0 < τ < T {0<\tau<T}

, to the homogeneous flow with clipped initial datum

min ⁡ { u 0 , 1 } {\min\{u_{0},1\}}

. We derive explicit estimates for the residual absorption term on positive time intervals and establish a global

L 1 {L^{1}}

-comparison framework for the positive-time dynamics. We also characterize the associated initial layer and show that its size is exactly given by the super-threshold part

( u 0 - 1 ) + {(u_{0}-1)_{+}}

of the initial datum. The global residual absorption is

O ⁢ ( 1 q ) {O(\frac{1}{q})}

away from

t = 0 {t=0}

. A quantitative bound for the solution error also contains the

L 1 {L^{1}}

continuity moduli of the homogeneous flow at the initial data; an unconditional

O ⁢ ( 1 q ) {O(\frac{1}{q})}

rate for the solution error is not asserted.