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In this paper, we study the non-linear diffusion equation associated with aparticle system where the common drift depends on the rate of absorption ofparticles at a boundary. We provide an interpretation as a structural creditrisk model with default contagion in a large interconnected banking system.Using the method of heat potentials, we derive a coupled system of Volterraintegral equations for the transition density and for the loss throughabsorption. An approximation by expansion is given for a small interactionparameter. We also present a numerical solution algorithm and conductcomputational tests.

Semi-analytical solution of a McKean-Vlasov equation with feedback through hitting a boundary