Quenching on the boundary

Numerical investigation of quenching for a nonlinear diffusion equation with a singular Neumann boundary condition

“…It is worth mentioning that for ␥ ϭ 1, these results had been established in [6]. However, from technical point of view, the results of [6] are somewhat different from those in [5].…”

“…However, from technical point of view, the results of [6] are somewhat different from those in [5]. On the one hand, in Theorem A of [6], no assumptions are imposed on the initial data, except the compatibility conditions. On the other hand, in Theorem B of [6], more restrictive conditions are assumed.…”

Instability of solutions of a semilinear heat equation with a Neumann boundary condition

“…Problems (1.2) and (1.3) have been intensively studied over the past few years. For details, see [1,3,4,6] and the references cited therein.…”

Quenching for a Semilinear Heat Equation With a Singular Boundary Outflux

“…As in [8], observe that in problem (1.1) the singular source term may become singular if u(x, t) → 1 − as (x, t) → (x * , T ), where x * is a quenching point in [0, 1] and T is a quenching time in (0, ∞). On the other hand, the outflux −u −β (1, t) may also become singular in some finite time (see [2], [3] and [9]). Here, we discuss the second situation.…”