An anomalous nonlinear heat-conduction problem (improvement)

A linear anomalous heat-flux problem is analysed from a stability point of view and a previous [Mathl Comput. Modelling 12(6), 671–672 (1989)] is improved. Then a non-linear problem proposed in the same paper is partly resolved and numerically verified, which shows that only one stationary solution is stable to perturbations.