Spatial decay estimates for a class of nonlinear parabolic equations via the maximum principle (Q1273283)

In 1976, \textit{C. O. Horgan} and \textit{L. T. Wheeler} [Z. Angew. Math. Phys. 27, 371-376 (1976; Zbl 0335.35055)] considered an alternative approach, based on maximum principles, for the derivation of pointwise spatial decay estimates of solutions to problems of classical linear heat conduction. The purpose of the present paper is to extend the work of Horgan and Wheeler and derive spatial decay estimates for equations of the form \[ \Delta u=h\bigl(u,|\nabla u|\bigr)u_t \] whose response is governed by the general nonlinear theory of heat conduction.