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The Kimura equation is a degenerated partial differential equation ofdrift-diffusion type used in population genetics. Its solution is required tosatisfy not only the equation but a series of conservation laws formulated asintegral constraints. In this work, we consider a population of two typesevolving without mutation or selection, the so-called neutral evolution. Weobtain explicit solutions in terms of Gegenbauer polynomials. To satisfy theintegral constraints it is necessary to prove new relations satisfied by theGegenbauer polynomials. The long-term in time asymptotic is also studied.

Solution of the Neutral Kimura equation with two integral constraints