The singular perturbation problem for a diffusion-advection equation

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The aim of this research project is to investigate the behavior of the solution of a diffusion-advection equation with the aid of the numerical analysis or the functional analysis. We considered at first the outline of the behavior through the numerical method. We had the numerical aspect under the useful suggestion of Professor Kawni (Chitose Science and technology University). Namely, there exists the wake after an obstacle and this was conjectured by the method of the investigation of an integral equation. This fact is not yet proved mathematically and it should be done. Each investigator considered his subject and made useful contribution.On the other hand, we investigated the behavior of the solution of the semilinear parabolic equation which is general case of a diffusion-advection equation. And we had several results. For example, we have the relation between the impulsive condition which describes the discontinuous phenomena and the stebility of the solution of the semilinear parabolic equation. And we see that the suitable impulsive condition makes a blowing-up solution stable and blows-up the solution at a desired time. We should investigate an original problem with the aid of these results.