Algebraic <g transform="matrix(.022,-0,0,-.022,.062,20.788)"><path id="x1D43F" d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z"></path></g> <g transform="matrix(.016,-0,0,-.016,12.862,10.025)"><path id="x32" d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z"></path></g> Decay for Weak Solutions of the Nonlinear Heat Equations in Whole Space R3 - Yang, Yuexing (Abstract and Applied Analysis, 2014)
We obtained the algebraic L2 time decay rate for weak solutionsof the nonlinear heat equations with the nonlinear term ∇u2u in whole space R3. Themethods are based on energy methods and Fourier analysis technique.