Problems of this type have been the subject of numerous investigations Ž w x. see for instance 1. In this paper we are interested in the situation when the reaction is very fast and so we shall be studying the limiting behaviour of the concentration profiles u and when the rate constant k tends to infinity.

We encountered this situation in a study of the penetration of radiolabeled antibodies into tumurous tissue, carried out for diagnostic as well w x as therapeutic purposes 3, 8. The dispersal represents the penetration, which is very slow on account of the large size of the antibodies and the reaction represents the attachment of antibodies to antigens in the tissue, which can be very fast. A major question is to determine the penetration depth as a function of time, since a good estimate of this quantity is essential for interpreting radio-images and assessing therapeutic effects. Ž. Ž.