We derive an adaptation of Li & 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 & Yau inequalities / Castorina, Daniele; Catino, Giovanni; Mantegazza, Carlo. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 1618-1891. - 202 827–850.:2(2023), pp. 827-850.
Semilinear Li & Yau inequalities
Daniele Castorina;Carlo Mantegazza
2023
Abstract
We derive an adaptation of Li & 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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