On the classical trapping problem

We consider the problem of finding the probability density for the location of an untrapped pest satisfying a diffusion equation with the scaled Laplacian. Then by taking the initial data to the diffusion process to be in some Lp spaces, we establish the existence and uniqueness of local solutions in these spaces and the existence and uniqueness of weak global solutions in Lp,q; p,q greater than 3. The interest of this method relies on the fact that it is by successive approximations and hence amenable to numerical treatment.