Messoud Efendiev, Vitali Vougalter
On the solvability of some systems of integro-differential equations with transport and concentrated sources
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ABSTRACT.  The article is devoted to the existence of solutions of a system of integro-differential equations involving the drift terms in the case of 
the normal diffusion and the influx/efflux terms proportional to the Dirac delta function. The proof of the existence of solutions is based on a fixed point technique. We use the solvability conditions for the non-Fredholm elliptic operators in unbounded domains. We emphasize that the study of the systems is more difficult than of the scalar case and requires to overcome more cumbersome technicalities.