Abstract: We study the Lp-asymptotic behavior of solutions to the heat equation on arbitrary rank Riemannian symmetric spaces of non-compact type G/K, for non-bi-K invariant initial data. We introduce certain mass functions that vary with p, and show that if the initial datum is continuous and compactly supported, then the solution to the heat equation converges in Lp norm to the mass function times the heat kernel. In the case of bi-K invariant initial data (previously considered by Vázquez, Anker et al, Naik et al), these functions boil down to constants related to the spherical transform of the initial datum. The Lp concentration of heat leads to significantly different expressions of the mass functions below or above the critical index p = 2.
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