On the spatial decay of solutions in the nonlinear theory of heat conduction

Edelstein (1971) has derived both integral and pointwise decay estimates for a semilinear heat equation that is based on Fourier's law. As an extension of Edelstein's work, spatial decay estimates are derived for solutions in a finite cylinder whose response is governed by the general nonlinear heat-conduction theory. The approach employed differs from Edelstein's approach in that the integral and pointwise estimates are obtained for the internal energy.