  In this paper, we study the non-linear diffusion equation associated with a
particle system where the common drift depends on the rate of absorption of
particles at a boundary. We provide an interpretation as a structural credit
risk model with default contagion in a large interconnected banking system.
Using the method of heat potentials, we derive a coupled system of Volterra
integral equations for the transition density and for the loss through
absorption. An approximation by expansion is given for a small interaction
parameter. We also present a numerical solution algorithm and conduct
computational tests.
