$L^p-L^q$ estimates for non-local heat and wave type equations on locally compact groups

Fuente: arXiv
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Main Authors: Cobos, Santiago Gómez, Restrepo, Joel E., Ruzhansky, Michael
Format: Preprint
Published: 2024
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author Cobos, Santiago Gómez
Restrepo, Joel E.
Ruzhansky, Michael
author_facet Cobos, Santiago Gómez
Restrepo, Joel E.
Ruzhansky, Michael
contents We prove the $L^p-L^q$ $(1<p\leqslant 2\leqslant q<+\infty)$ norm estimates for the solutions of heat and wave type equations on a locally compact separable unimodular group $G$ by using an integro-differential operator in time and any positive left invariant operator (maybe unbounded) on $G$. We complement our studies by giving asymptotic time estimates for the solutions, which in some cases are sharp.
format Preprint
id arxiv_https___arxiv_org_abs_2405_00731
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle $L^p-L^q$ estimates for non-local heat and wave type equations on locally compact groups
Cobos, Santiago Gómez
Restrepo, Joel E.
Ruzhansky, Michael
Analysis of PDEs
43A15, 43A85, 45K05
We prove the $L^p-L^q$ $(1<p\leqslant 2\leqslant q<+\infty)$ norm estimates for the solutions of heat and wave type equations on a locally compact separable unimodular group $G$ by using an integro-differential operator in time and any positive left invariant operator (maybe unbounded) on $G$. We complement our studies by giving asymptotic time estimates for the solutions, which in some cases are sharp.
title $L^p-L^q$ estimates for non-local heat and wave type equations on locally compact groups
topic Analysis of PDEs
43A15, 43A85, 45K05
url https://arxiv.org/abs/2405.00731