2015/05/11 by Rolando Magnanini, Michele Marini, Magnanini, Rolando +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP
paper · pdf · doi:10.48550/arxiv.1505.02638
arxiv created 2015/05/11 · arxiv updated 2015/05/12
We characterize all the solutions of the heat equation that have their (spatial) equipotential surfaces which do not vary with the time. Such solutions are either isoparametric or split in space-time. The result gives a final answer to a problem raised by M. S. Klamkin, extended by G. Alessandrini, and that was named the Matzoh Ball Soup Problem by L. Zalcman. Similar results can also be drawn for a class of quasi-linear parabolic partial differential equations with coefficients which are homogeneous functions of the gradient variable. This class contains the (isotropic or anisotropic) evolution p-Laplace and normalized p-Laplace equations.