{"type":"journal_article","volume":2025,"publication_identifier":{"issn":["1073-7928","1687-0247"]},"date_created":"2026-01-06T09:45:00Z","date_updated":"2026-01-06T09:45:12Z","intvolume":"      2025","abstract":[{"text":"<jats:title>Abstract</jats:title>\n               <jats:p>The main goal of this work is to study the $L^{p}$-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. For initial data $u_{0}$ compactly supported or in a weighted $L^{1}(G/K)$ space with a weight depending on $p\\in [1, \\infty ]$, we introduce a mass function $M_{p}(u_{0})(\\cdot )$, and prove that if $h_{t}$ is the heat kernel on $G/K$, then $$ \\begin{align*} &amp;\\|h_t\\|_p^{-1}\\,\\|u_0\\ast h_t \\, - \\,M_p(u_0)(\\cdot)\\,h_t\\|_p \\rightarrow 0 \\quad \\textrm{as} \\quad t\\rightarrow \\infty.\\end{align*} $$ Interestingly, the $L^{p}$ heat concentration leads to completely different expressions of the mass function for $1\\leq p &amp;lt;2$ and $2\\leq p\\leq \\infty $. If we further assume that the initial data are bi-$K$-invariant, then our mass function boils down to the constant $\\int _{G/K}u_{0}$ in the case $p=1$, and more generally to $\\mathcal{H}{u_{0}}(i\\rho (2/p-1))$ if $1\\leq p&amp;lt;2$, and to $\\mathcal{H}{u_{0}}(0)$ if $2\\leq p \\leq \\infty $. Thus, we improve upon results by Vázquez, Anker et al., and Naik et al., clarifying the nature of the problem.</jats:p>","lang":"eng"}],"language":[{"iso":"eng"}],"publication_status":"published","doi":"10.1093/imrn/rnaf074","author":[{"first_name":"Effie","last_name":"Papageorgiou","full_name":"Papageorgiou, Effie"}],"status":"public","user_id":"100325","publication":"International Mathematics Research Notices","publisher":"Oxford University Press (OUP)","article_number":"rnaf074","issue":"7","year":"2025","citation":{"apa":"Papageorgiou, E. (2025). <i>L</i>           p Asymptotics for the Heat Equation on Symmetric Spaces for Non-symmetric Solutions. <i>International Mathematics Research Notices</i>, <i>2025</i>(7), Article rnaf074. <a href=\"https://doi.org/10.1093/imrn/rnaf074\">https://doi.org/10.1093/imrn/rnaf074</a>","chicago":"Papageorgiou, Effie. “<i>L</i>           p Asymptotics for the Heat Equation on Symmetric Spaces for Non-Symmetric Solutions.” <i>International Mathematics Research Notices</i> 2025, no. 7 (2025). <a href=\"https://doi.org/10.1093/imrn/rnaf074\">https://doi.org/10.1093/imrn/rnaf074</a>.","short":"E. Papageorgiou, International Mathematics Research Notices 2025 (2025).","bibtex":"@article{Papageorgiou_2025, title={<i>L</i>           p Asymptotics for the Heat Equation on Symmetric Spaces for Non-symmetric Solutions}, volume={2025}, DOI={<a href=\"https://doi.org/10.1093/imrn/rnaf074\">10.1093/imrn/rnaf074</a>}, number={7rnaf074}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Papageorgiou, Effie}, year={2025} }","ama":"Papageorgiou E. <i>L</i>           p Asymptotics for the Heat Equation on Symmetric Spaces for Non-symmetric Solutions. <i>International Mathematics Research Notices</i>. 2025;2025(7). doi:<a href=\"https://doi.org/10.1093/imrn/rnaf074\">10.1093/imrn/rnaf074</a>","ieee":"E. Papageorgiou, “<i>L</i>           p Asymptotics for the Heat Equation on Symmetric Spaces for Non-symmetric Solutions,” <i>International Mathematics Research Notices</i>, vol. 2025, no. 7, Art. no. rnaf074, 2025, doi: <a href=\"https://doi.org/10.1093/imrn/rnaf074\">10.1093/imrn/rnaf074</a>.","mla":"Papageorgiou, Effie. “<i>L</i>           p Asymptotics for the Heat Equation on Symmetric Spaces for Non-Symmetric Solutions.” <i>International Mathematics Research Notices</i>, vol. 2025, no. 7, rnaf074, Oxford University Press (OUP), 2025, doi:<a href=\"https://doi.org/10.1093/imrn/rnaf074\">10.1093/imrn/rnaf074</a>."},"title":"<i>L</i>\n          p Asymptotics for the Heat Equation on Symmetric Spaces for Non-symmetric Solutions","_id":"63505"}