A study of some problems arising from combustion and microwave heating

A model for microwave heating is considered. The behaviour of the solution is analysed and a procedure to calculate the solution is presented. This procedure is based on an eigenfunction expansion. Combining both analytical argument and numerical results, it is then shown that the qualitative behaviour of the solution can be deduced from the fundamental-mode. An extension to a model of porous medium combustion is presented. It is again shown that the qualitative behaviour of the solution is captured by the first eigenmode. The corresponding model for traveling combustion waves is examined and a numerical solution is sought. The algorithm for computation is based on a shooting method used in an existence proof. The idea is to cut the infinite domain into two semi-infinite intervals and apply the shooting technique on both sides. This two-sided shooting method is then applied to compute traveling combustion waves of a solid material.