We consider the problem \[ ( P ) { u t = ( u m ) x x , u ( x , 0 ) = u 0 ( x ) with x ∈ R , t > 0 for x ∈ R \left ( {\text {P}} \right )\quad \quad \left \{ {\begin {array}{*{20}{c}} {{u_t} = {{({u^m})}_{xx}},} \\ {u(x,0) = {u_0}(x)} \\ \end {array} } \right .\quad \begin {array}{*{20}{c}} {{\text {with}}\,x \in {\mathbf {R}},\,t > 0} \\ {{\text {for}}\,x \in {\mathbf {R}}} \\ \end {array} \] where m > 1 m > 1 and u 0 {u_0} is a continuous, nonnegative function that vanishes outside an interval ( a , b ) (a,\,b) and such that ( u 0 m − 1 ) ≤ − C ≤ 0 (u_0^{m - 1}) \leq - C \leq 0 in ( a , b ) (a,\,b) . Using a Trotter-Kato formula we show that the solution conserves the concavity in time: for every t > 0 , u ( x , t ) t > 0,\,u(x,t) vanishes outside an interval Ω ( t ) = ( ζ 1 ( t ) , ζ 2 ( t ) ) \Omega (t) = ({}_{\zeta 1}(t),\,{}_{\zeta 2}(t)) and \[ ( u m − 1 ) x x ≤ − C 1 + C ( m ( m + 1 ) / ( m − 1 ) ) t {({u^{m - 1}})_{xx}} \leq - \frac {C} {{1 + C(m(m + 1)/(m - 1))t}} \] in Ω ( t ) \Omega (t) . Consequently the interfaces x = ζ i ( t ) x{ = _{\zeta i}}(t) , i = 1 , 2 i = 1,\,2 , are concave curves. These results also give precise information about the large time behavior of solutions and interfaces.