Identifiability of the nonlinearity in a quasilinear parabolic system
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One-dimensional unsteady-state heat conduction is governed by a second-order quasilinear parabolic equation. The nonlinearity arises from the temperature dependence of the thermal conductivity and/or specific heat. The author shows that measurement of temperature and heat flux at only one boundary point can uniquely determine the thermal conductivity as a function of temperature when the specific heat is known or the specific heat as a function of temperature when the thermal conductivity is known.