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arXiv · 2405.00731

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

Santiago Gómez Cobos·Joel E. Restrepo·Michael Ruzhansky
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Abstract

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.

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Santiago Gómez Cobos, Joel E. Restrepo, Michael Ruzhansky. 2024-04-28. $L^p-L^q$ estimates for non-local heat and wave type equations on locally compact groups. https://arxiv.org/abs/2405.00731

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