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 Maria. - 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.
2023
Semilinear Li & Yau inequalities / Castorina, Daniele; Catino, Giovanni; Mantegazza, Carlo Maria. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 1618-1891. - 202 827–850.:2(2023), pp. 827-850.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/868403
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