April 28, 2024Open Access

Lᵖ-Lq estimates for non-local heat and wave type equations on locally compact groups

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Abstract

We prove the Lᵖ-Lq (1<p 2 q<+) 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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Cobos et al. (Sun,) studied this question.

synapsesocial.com/papers/68e6d417b6db6435876515c7 https://doi.org/https://doi.org/10.48550/arxiv.2405.00731

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