ConstantineM.Dafermoshasdoneextensiveresearchattheinterfaceofpartialdifferentialequationsandcontinuumphysics.Heisaworldleaderinnonlinearhyperbolicconservationlaws,whereheintroducedseveralfundamentalmethodsinthesubjectincludingthemethodsofrelativeentropy,generalizedcharacteristics,andwave-fronttracking,aswellastheentropyratecriterionfortheselectionofadmissiblewavefans.Hehasalsomadefundamentalcontributionsonthemathematicaltheoryoftheequationsofthermomechanicsasitpertainsinmodelingandanalysisofmaterialswithmemory,thermoelasticity,andthermoviscoelasticity.Hisworkisdistinctlycharacterizedbyanunderstandingofthefundamentalissuesofcontinuumphysicsandtheirroleindevelopingnewtechniquesofmathematicalanalysis.
