Authors establish initial-condition criteria for left- or right-boundary quenching in the equation (ϕ(u))_t = (|u_x|^{r-2}u_x)_x with the given singular BCs and derive explicit rates and time bounds when ϕ(u)=u and r=2, backed by numerics.
Kawarada, On solutions of initial-boundary problem for ut = uxx + 1 1− u , Publ
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Quenching estimates for a non-Newtonian filtration equation with singular boundary conditions
Authors establish initial-condition criteria for left- or right-boundary quenching in the equation (ϕ(u))_t = (|u_x|^{r-2}u_x)_x with the given singular BCs and derive explicit rates and time bounds when ϕ(u)=u and r=2, backed by numerics.