Continuous dependence on the heat source and non‐linear stability for convection with internal heat generation

Source abstract

Abstract It is shown that the solution to the boundary‐initial value problem for a heat‐conducting viscous fluid depends continuously on changes in the heat supply function, for the improperly posed backward in time problem. A non‐linear convection threshold is also determined for the problem of a layer of fluid heated internally (non‐uniformly), with zero neat flux on the lower boundary and constant‐temperature upper surface.