We obtained the algebraic time decay rate for weak solutions of the nonlinear heat equations with the nonlinear term in whole space . The methods are based on energy methods and Fourier analysis technique.
Yuexing Yang. "Algebraic Decay for Weak Solutions of the Nonlinear Heat Equations in Whole Space R 3." Abstr. Appl. Anal. 2014 (SI47) 1 - 4, 2014. https://doi.org/10.1155/2014/329474