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In this paper substantiated for a differential equation of pseudoparabolic type with discontinuous coefficients a final-boundary problem with non-classical boundary conditions is considered, which requires no matching conditions. The considered equation as a pseudoparabolic equation generalizes not only classic equations of mathematical physics (heatconductivity equations, string vibration equation) and also many models differential equations ( telegraph equation, Aller's equation , moisturedoi:10.11648/j.acm.20130203.15 fatcat:wajmntcq7newzjufknhaaddwvu