Sufficient and necessary initial mass conditions for the existence of a waiting time in nonlinear-convection processes (Q810289)

The authors consider a diffusion-convection equation in one space dimension which gives rise to free boundaries separating regions where the solution vanishes from those where it is positive. Using a mass comparison principle, the authors derive necessary and sufficient conditions for the occurrence of waiting times at the fronts. Depending on the actual values of the parameters m,\(\lambda\) in the equation \(u_ t=(u^ m)_{xx}+b(u^{\lambda})_ x\), very different results are obtained.