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arXiv · 2210.05608

Heat and wave type equations with non-local operators, I. Compact Lie groups

Wagner A. A. de Moraes·Joel E. Restrepo·Michael Ruzhansky
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Abstract

We prove existence, uniqueness and give the analytical solution of heat and wave type equations on a compact Lie group $G$ by using a non-local (in time) differential operator and a positive left invariant operator (maybe unbounded) acting on the group. For heat type equations, solutions are given in $L^q(G)$ for data in $L^p(G)$ with $1<p\leqslant 2\leqslant q<+\infty$. We also provide some asymptotic estimates (large-time behavior) for the solutions. Some examples are given. Also, for wave type equations, we give the solution on some suitable Sobolev spaces over $L^2(G)$. We complement our results, by studying a multi-term heat type equation as well.

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Wagner A. A. de Moraes, Joel E. Restrepo, Michael Ruzhansky. 2023-01-20. Heat and wave type equations with non-local operators, I. Compact Lie groups. https://doi.org/10.1093/imrn%2Frnad017

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