$L^p-L^q$ estimates for non-local heat and wave type equations on locally compact groups
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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2024
- DOI:
- 10.48550/arXiv.2405.00731
- arXiv:
- arXiv:2405.00731
- Bibcode:
- 2024arXiv240500731G
- Keywords:
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- Mathematics - Analysis of PDEs;
- 43A15;
- 43A85;
- 45K05
- E-Print:
- The paper has been accepted for publication in the journal "Comptes Rendus Math\'{e}matique". arXiv admin note: substantial text overlap with arXiv:2302.00721