We derive an adaptation of Li and Yau estimates for positive solutions of semilinear heat equations on Riemannian manifolds with nonnegative Ricci tensor. We then apply these estimates to obtain a Harnack inequality and to discuss monotonicity, convexity, decay estimates and triviality of ancient and eternal solutions.
Semilinear Li and Yau inequalities / Castorina, D., Catino, G., Mantegazza, C.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 202:2(2023), pp. 827-850. [10.1007/s10231-022-01261-3]
Semilinear Li and Yau inequalities
Castorina D.;Catino G.;Mantegazza C.
2023
Abstract
We derive an adaptation of Li and Yau estimates for positive solutions of semilinear heat equations on Riemannian manifolds with nonnegative Ricci tensor. We then apply these estimates to obtain a Harnack inequality and to discuss monotonicity, convexity, decay estimates and triviality of ancient and eternal solutions.File in questo prodotto:
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